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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 12 Circles

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 12 – Circles

Chapter 12 – Circles Exercise Ex. 12A

Question 1

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of a chord from the centre of the circle.

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 2

Prove that the diameter of the circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it.

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 3

Prove that two different circles cannot intersects other at more than two points.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 4

Two circle of the radii 10 cm and 8 cm intersects each other , and the length of the common chord is 12 cm. Find the distance between their centres.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 5

Two equal circle intersects in P and Q. A straight line through P meets the circles in A and B. Prove that QA= QB.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 6

If a diameter of the circle bisects each of the two chords of a circle then prove that the chords are parallel.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 7

In the adjoining figure , two circles with centres at A and B, and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q . Find the length of PQ.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 8

In the given figure , AB is a chord of a circle with centre O and AB is produced to C such that BC=OB. Also CO is a joined and produced to meet the circle in D. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, prove that x=3y.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 9

AB and AC are two chords of a
circle of radius r such that AB = 2AC. If p and q are the distances of AB and
AC from the centre then prove that 4q2 =
p2 + 3r2.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Let
O be the centre of a circle with radius r.

OB = OC = r

Let
AC = x

Then,
AB = 2x

Let
OM
⊥ AB

OM = p

Let
ON
⊥ AC

ON = q

In
ΔOMB, by
Pythagoras theorem,

OB2
= OM2 + BM2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

In
ΔONC, by
Pythagoras theorem,

OC2
= ON2 + CN2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 10

In the adjoining figure , O is the centre of a circle . If AB and AC are chordsof a circlesuch thatAB=AC, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, prove that PB=QC.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 11

In the adjoining figure, BC is a diameter of a circle with circle with centre O. If AB and CD are two chords such that AB|| CD, prove that AB=CD.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 12

Find the length of the chord which is at the distance of 3 cm from the centre of a circle of radius 5 cm.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 13

An equilateral triangle of side 9 cm is inscribed in a circle . Find the radius of the circle.

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 15

In the adjoining figure , OPQR is a square. A circle drawn with centre O cuts the square in X and Y. prove that QX =QY.

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

Question 16

Two circle with centres O and O’ intersect at two points A and B. A line
PQ is drawn parallel to OO’ through A or B, intersecting the circles at P and
Q. Prove that PQ = 2OO’.

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Draw
OM
⊥ PQ and O’N ⊥ PQ

OM ⊥ AP

AM = PM (perpendicular from the centre of a circle bisects the chord)

AP = 2AM ….(i)

And,
O’N
⊥ PQ

O’N ⊥ AQ

AN = QN (perpendicular from the centre of a circle bisects the chord)

AQ = 2AN ….(ii)

Now,

PQ = AP + PQ

PQ = 2AM + 2AN

PQ = 2(AM + AN)

PQ = 2MN

PQ = 2OO’  (since MNO’O is a rectangle)

Question 17

A chord of length 30 cm is drawn at a distance of 8 cm from the centre of a circle. Find the radius of the circle.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 18

In a circle of radius 5 cm, AB and CD are two parallel chords of lengths 8 cm and 6cm respectively. Calculate the distance between the chords if they are

(i) On the same side of the centre

(ii) On the opposite side of the centre.

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 19

Two parallel chords of lengths 30 cm and 16 cm are drawn on the opposite sides of the centre of a circle of a radius 17 cm. Find the distance between the chords.

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 20

In the given figure , the diameter CD of a circle with centre O is perpendicular to chord AB. If AB=12 cm and CE=3cm, calculate the radius of the circle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 21

In the given figure, a circle with centre O is given in which a diameter AB bisects the chord CD at a point E such that CE=ED=8 cm and EB=4 cm. Find the radius of the circle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

 

 

Question 22

In the adjoining figure, OD is perpendicular to the chord AB of a circle with centre O. If BC is a diameter, show that AC||DO and AC=2xOD.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 23

In the given figure, O is the centre of a circle in which chords AB and CD intersect at P such that PO bisects R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles. Prove that AB=CD.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Chapter 12 – Circles Exercise Ex. 12B

Question 1

(i) In figure (1) , O is the centreof the circle . If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles(ii) In figure(2), A, B and C are three points on the circlewithcentre O such that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles .

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 2

In the given figure , O is the centre of a circle, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles , find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 3

In the adjoining figure , chords AC and BD of a circle with centre O, intersect at right angles at E. if  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, calculate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 4

In the given figure , O is the centre of a circle in which R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.  Find  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Solution 4

   R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 5

In the given figure, O is the centre of the circle and ∠BCO
= 30°.
Find x and y.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 5

Given,
∠AOD = 90° and ∠OEC = 90°

∠AOD = ∠OEC

But
∠AOD and ∠OEC are corresponding
angles.

OD || BC and OC is
the transversal.

∠DOC = ∠OCE (alternate angles)

∠DOC = 30° (since ∠OCE = 30°)

We
know that the angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a
point on the circumference.

∠DOC = 2∠DBC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Now,
∠ABE = ∠ABC = ∠ABD + ∠DBC = 45° + 15° = 60°

In
ΔABE,

BAE + ∠AEB + ∠ABE = 180°

x + 90° + 60° = 180°

x + 150° = 180°

x = 30°

Question 6

In the given figure, O is the centre of the circle, BD = OD and CD
AB. Find ∠CAB

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 6

Construction:
Join AC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Given,
BD = OD

Now,
OD = OB (radii of same circle)

BD = OD = OB

ΔODB is an
equilateral triangle.

∠ODB = 60°

We
know that the altitude of an equilateral triangle bisects the vertical angle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Now,
∠CAB = ∠BDC (angles in the same segment)

∠CAB = ∠BDE = 30°

Question 7

In the given figure, PQ is a diameter of a circle with centre O. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 8

In the figure given below, P and Q
are centres of two circles, intersecting at B and
C, and ACD is a straight line.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 8

We know that the angle
subtended by an arc of a circle at its centre is
twice the angle subtended by the same arc at a point on the circumference.

∠APB = 2∠ACB

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Now, ACD is a straight
line.

∠ACB + ∠DCB = 180°

75° + ∠DCB = 180°

∠DCB = 105°

Again,

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 9

In the given figure , R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles. Show that BC is equal to the radius of the circumcircle of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles whose centre is O.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 9

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

 

Question 10

In the given figure, AB and CD are
two chords of a circle, intersecting each other at a point E. Prove that

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 10

Join
AC and BC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

We
know that the angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a
point on the circumference.

∠AOC = 2∠ABC ….(i)

Similarly,
∠BOD = 2∠BCD ….(ii)

Adding
(i) and (ii),

AOC + ∠BOD = 2∠ABC + 2∠BCD

∠AOC + ∠BOD = 2(∠ABC + ∠BCD)

∠AOC + ∠BOD = 2(∠EBC + ∠BCE)

∠AOC + ∠BOD = 2(180° – ∠CEB)

∠AOC + ∠BOD = 2(180° – [180° – ∠AEC])

∠AOC + ∠BOD = 2∠AEC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 11

In the given figure, O is the centre of the circle and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles .

Calculate the value of  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles .

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Solution 11

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

 

Question 12

In the given figure , O is the centre of the circle .If  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles , find the value of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 13

In the given figure , O is the centre of the circle. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 13

 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 14

In the given figure, O is the centre of the circle .If  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 14

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 15

In the given figure , R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, calculate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 16

In the adjoining figure , DE is a chord parallel to diameter AC of the circle with centre O. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, calculate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 17

In the adjoining figure, O is the centre of the circle. Chord CD is parallel to diameter AB. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles  calculate R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Solution 17

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 18

In the given figure, AB and CD are straight lines through the centre O of a circle. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles , find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 18

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Chapter 12 – Circles Exercise Ex. 12C

Question 1

In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles .

Find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 2

In the given figure, O is the centre of the circle and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles. Calculate the vales of x and y.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 2

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

 

Question 3

In the given figure , sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles find the value of x.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 4

In the given figure, AB is a diameter of a circle with centre O and DO||CB. If  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, calculate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Also , show that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles is an equilateral triangle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 5
Two chord AB and CD of a circle intersects each other at P outside the circle. If AB=6cm, BP=2cm and PD=2.5 cm, Find CD.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 6

In the given figure , O is the centre of a circle. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles , calculate

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 7

In the given figure, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles is an isosceles triangle in which AB=AC and a circle passing through B and C intersects AB and AC at D and E respectively. Prove that DE || BC.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 8

In the given figure, AB and CD are two parallel chords of a circle . If BDE and ACE are straight lines , intersecting at E, prove that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles is isosceles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 8

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 9

In the given figure, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles Find the values of x and y.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 10

In the given figure , ABCD is a quadrilateral in which AD=BC and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.  Show that the pints A, B, C, D lie on a circle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 11

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 12

In the given figure, POQ is a diameter and PQRS is a cyclic quadrilateral. If R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 13

Prove that the circles described with the four sides of a rhombus . as diameter , pass through the point of intersection of its diagonals.

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 14

ABCD is a rectangle . Prove that the centre of the circle through A, B, C, D is the point of intersection of its diagonals.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 15

Give a geometrical construction for finding the fourth point lying on a circle passing through three given points , without finding the centre of the circle. Justify the construction.

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 16

In a cyclic quadrilateral ABCD, if R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles, show that the smaller of the two is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 17

The diagonal s of a cyclic quadrilateral are at right angles . Prove that perpendicular from the point of their intersection on any side when produced backwards, bisects the opposite side.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 18

On a common hypotenuse AB, two
right triangles ACB and ADB are situated on opposite sides. Prove that
∠BAC
= ∠BDC.

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

AB
is the common hypotenuse of
ΔACB and ΔADB.

ACB = 90° and BDC = 90°

ACB + BDC =
180
°

The opposite
angles of quadrilateral ACBD are supplementary.

Thus,
ACBD is a cyclic quadrilateral.

This
means that a circle passes through the points A, C, B and D.

BAC = BDC (angles in the same segment)

Question 19

ABCD is a quadrilateral such that
A is the centre of the circle passing through B, C
and D. Prove that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 19

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Construction:
Take a point E on the circle. Join BE, DE and BD.

We
know that the angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a
point on the circumference.

∠BAD = 2∠BED

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Now,
EBCD is a cyclic quadrilateral.

BED + BCD =
180
°

BCD =
180
°BED

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

In ΔBCD, by
angle sum property

CBD + CDB + BCD =
180
°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

Question 20

In the given figure , O is the centre of the circle and arc ABC subtends an angle of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circlesat the centre . If AB is extended to P, find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 21

In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced . If  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 22

In the given figure, BD=DC and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 23

In the given figure, O is the centre of the given circle and measure of arc ABC is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles Determine R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 24

In the given figure, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles is equilateral. Find R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 25

In the adjoining figure, ABCD is a cyclic quadrilateral in which R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 26

In the given figure , O is the centre of a circle and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - CirclesFind the values of x and y.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Chapter 12 – Circles Exercise MCQ

Question 1

The radius of a circle is 13 cm and
the length of one of its chords is 10 cm. The distance of the chord from the
centre is

  1. 11.5 cm
  2. 12 cm
  3. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles
  4. 23 cm
Solution 1

Correct option: (b)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 2

In the given figure, BOC is a diameter of a circle with
centre O. If AB and CD are two chords such that AB

CD. If AB = 10 cm, then CD =?

  1. 5 cm
  2. 12.5 cm
  3. 15 cm
  4. 10 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 3

In the given figure, AB is a chord of a circle with centre
O and AB is produced to C such that BC = OB. Also, CO is joined and produced
to meet the circle in D. If
∠ACD = 25°,
then ∠AOD
=?

  1. 50°
  2. 75°
  3. 90°
  4. 100°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 4

In the given figure, AB is a chord
of a circle with centre O and BOC is a diameter. If OD

AB such that OD = 6 cm, then AC =?

  1. 9 cm
  2. 12 cm
  3. 15 cm
  4. 7.5 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 5

An equilateral triangle of side 9
cm is inscribed in a circle. The radius of the circle is

  1. 3 cm
  2. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles
  3. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles
  4. 6 cm
Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 6

 The angle in a semicircle measures

  1. 45°
  2. 60°
  3. 90°
  4. 36°
Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 7

Angles in the same segment of a
circle area are

  1. equal
  2. complementary
  3. supplementary
  4. none of these
Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 8

In the given figures, ⧍ABC
and ⧍DBC
are inscribed in a circle such that ∠BAC = 60°
and ∠DBC
= 50°.
Then, ∠BCD
=?

  1. 50°
  2. 60°
  3. 70°
  4. 80°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 9

In the given figure, BOC is a
diameter of a circle with centre O. If
∠BCA = 30°,
then ∠CDA
=?

  1. 30°
  2. 45°
  3. 60°
  4. 50°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 10

In the given figure, O is the centre of a circle. If
∠OAC
= 50°,
then ∠ODB
=?

  1. 40°
  2. 50°
  3. 60°
  4. 75°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 11

In the given figure, O is the centre of a circle in which ∠OBA
= 20°
and ∠OCA
= 30°.
Then, ∠BOC
=?

  1. 50°
  2. 90°
  3. 100°
  4. 130°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 12

A chord is at a distance of 8 cm from the centre of a
circle of radius 17 cm. The length of the chord is

  1. 25 cm
  2. 12.5 cm
  3. 30 cm
  4. 9 cm
Solution 12

Correct option: (c)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 13

In the given figure, O is the centre of a circle. If ∠AOB
= 100°
and ∠AOC
= 90°,
then ∠BAC
=?

  1. 85°
  2. 80°
  3. 95°
  4. 75°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 14

In the given figure, O is the
centre of a circle. Then,
∠OAB =?

  1. 50°
  2. 60°
  3. 55°
  4. 65°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 15

In the given figure, O is the centre of a circle and ∠AOC
= 120°.
Then, ∠BDC
=?

  1. 60°
  2. 45°
  3. 30°
  4. 15°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 16

In the given figure, O is the
centre of a circle and
∠OAB = 50°.
Then, ∠CDA
=?

  1. 40°
  2. 50°
  3. 75°
  4. 25°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 17

In the given figure, AB and CD are two intersecting chords
of a circle. If
∠CAB = 40°
and ∠BCD
= 80°,
then ∠CBD
=?

  1. 80°
  2. 60°
  3. 50°
  4. 70°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 18

In the given figures, O is the centre of a circle and
chords AC and BD intersect at E. If
∠AEB = 110°
and ∠CBE
= 30°,
then ∠ADB
=?

  1. 70°
  2. 60°
  3. 80°
  4. 90°R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 19

In the given figure, O is the
centre of a circle in which
∠OAB =20°
and ∠OCB
= 50°.
Then, ∠AOC
=?

  1. 50°
  2. 70°
  3. 20°
  4. 60°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 20

In
the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ∠ADC
= 120°,
then ∠BAC
=?

  1. 60°
  2. 30°
  3. 20°
  4. 45°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 21

In the given figure ABCD is a cyclic quadrilateral in which
AB

DC and ∠BAD
= 100°.
Then ∠ABC
=?

  1. 80°
  2. 100°
  3. 50°
  4. 40°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 22

In the given figure, O is the
centre of a circle and
∠AOC =130°.
Then, ∠ABC
=?

  1. 50°
  2. 65°
  3. 115°
  4. 130°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 23

In the given figure, BOC is a diameter of a circle and AB =
AC. Then
∠ABC =?

  1. 30°
  2. 45°
  3. 60°
  4. 90°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 24

In the given figure, AOB is a
diameter of a circle and CD AB. If
∠BAD = 30°,
then ∠CAD
=?

  1. 30°
  2. 60°
  3. 45°
  4. 50°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 25

In the given figure, O is the
centre of a circle in which
∠AOC =100°.
Side AB of quad. OABC has been produced to D. Then, ∠CBD =?

  1. 50°
  2. 40°
  3. 25°
  4. 80°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 26

In the given figure, O is the
centre of a circle and
∠OAB = 50°.
Then, ∠BOD=?

  1. 130°
  2. 50°
  3. 100°
  4. 80°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 27

In the given figures, ABCD is a cyclic quadrilateral in
which BC = CD and
∠CBD = 35°.
Then, ∠BAD
=?

  1. 65°
  2. 70°
  3. 110°
  4. 90°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 28

In the given figure, equilateral
ABC is inscribed in a circle and ABCD is a quadrilateral, as shown. Then ∠BDC
=?

  1. 90°
  2. 60°
  3. 120°
  4. 150°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 29

In the give figure, side Ab and AD of quad. ABCD are
produced to E and F respectively. If
∠CBE = 100°,
then ∠CDF
=?

  1. 100°
  2. 80°
  3. 130°
  4. 90°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 30

In the given figure, O is the centre of a circle and ∠AOB
= 140°.
The, ∠ACB
=?

  1. 70°
  2. 80°
  3. 110°
  4. 40°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 31

In the given figure, O is the
centre of a circle and
∠AOB = 130°.
Then, ∠ACB
=?

  1. 50°
  2. 65°
  3. 115°
  4. 155°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 32

In the given figure, ABCD and ABEF
are two cyclic quadrilaterals. If
∠BCD = 110°,
then ∠BEF
=?

  1. 55°
  2. 70°
  3. 90°
  4. 110°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 33

 In the given figure,
ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn
parallel to AB such that
∠ADC = 95°
and ∠ECF
=20°.
Then, ∠BAD
=?

  1. 95°
  2. 85°
  3. 105°
  4. 75°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 34

In the given figure, O is the centre of a circle and ∠ACB = 30°. Then, ∠AOB =?

  1. 30°
  2. 15°
  3. 60°
  4. 90°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

Question 35

Two chords AB and CD of a circle intersect each other at a point E outside the circle. If AB = 11 cm, BE = 3 cm and DE = 3.5 cm, then CD =?

  1. 10.5 cm
  2. 9.5 cm
  3. 8.5 cm
  4. 7.5 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 36

In the given figure, A and B are
the centres of two circles having radii 5 cm and 3 cm respectively and
intersecting at points P and Q respectively. If AB = 4 cm, then the length of
common chord PQ is

  1. 3 cm
  2. 6 cm
  3. 7.5 cm
  4. 9 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 37

In the given figure, ∠AOB = 90° and ∠ABC = 30°. Then ∠CAO =?

  1. 30°
  2. 45°
  3. 60°
  4. 90°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 38

In the given figure, O is the centre of a circle. If ∠OAB
= 40°
and C is a point on the circle, then ∠ACB =?

  1. 40°
  2. 50°
  3. 80°
  4. 100°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 39

In the given figure, AOB is a diameter of a circle with
centre O such that AB = 34 cm and CD is a chord of length 30 cm. Then, the
distance of CD from AB is

  1. 8 cm
  2. 15 cm
  3. 18 cm
  4. 6 cm

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 40

AB and CD are two equal chords of a circle with centre O
such that
∠AOB = 80°, then ∠COD
=?

  1. 100°
  2. 80°
  3. 120°
  4. 40°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 41

In the given figure, CD is the diameter of a circle with
centre O and CD is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm,
then radius of the circle is

  1. 6 cm
  2. 9 cm
  3. 7.5 cm
  4. 8 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Question 42

In the given figure, O is the centre of a circle and
diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB
= 4 cm. The radius of the circle is

  1. 10 cm
  2. 12 cm
  3. 6 cm
  4. 8 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

Solution 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Circles

 

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