# NCERT solution class 10 chapter 10 Circles exercise 10.1 mathematics

## EXERCISE 10.1

#### Question 1:

How many tangents can a circle have?

A circle can have infinite tangents.

#### Question 2:

Fill in the blanks:

(i) A tangent to a circle intersects it in _______ point (s).

(ii) A line intersecting a circle in two points is called a __________.

(iii) A circle can have __________ parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called ____.

(i) One

(ii) Secant

(iii) Two

(iv) Point of contact

#### Question 3:

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

(A) 12 cm. (B) 13 cm (C) 8.5 cm (D)  cm test

We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.

OP PQ

By applying Pythagoras theorem in Î”OPQ,

OP+ PQ= OQ

52 + PQ=12

PQ=144 âˆ’ 25

PQ = cm.

Hence, the correct answer is (D).

#### Question 4:

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.