These NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 10 Maths Chapter 10 Circles Exercise 10.1

Question 1.

How many tangents can a circle have?

Solution:

There can be infinitely many tangents to a circle.

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 ……….. .

Solution:

(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) \( \sqrt{199} \) cm

Solution:

We have given that PQ is a tangent of a circle whose centre is O are radius 5 cm. Length of OQ = 12 cm.

We know that, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

OQ = 12 cm

∴ ∠OPQ = 90°

[The tangent to a circle is perpendicular to the radius through the point of contact]

PQ^{2} = OQ^{2} – OP^{2} [By Pythagoras theorem]

PQ^{2} = 12^{2} – 5^{2} = 144 – 25 = 199

∴ PQ = \( \sqrt{199} \) cm.

Hence correct option 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.

Solution:

PQ is a tangent and LM a secant.