## NCERT Solutions for Class 10 Maths Chapter 10 – Circles

**Exercise: 10.1**

1. How many tangents can a circle have?

**Answer**

A circle can have infinite tangents.

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 ............

**Answer**

(i) one

(ii) secant

(iii) two

(iv) point of contact

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 point Q so that OQ = 12 cm. Length PQ is :

(A) 12 cm

(B) 13 cm

(C) 8.5 cm

(D) √119 cm

(B) 13 cm

(C) 8.5 cm

(D) √119 cm

**Answer**

∴ OP ⊥ PQ

By Pythagoras theorem in ΔOPQ,

OQ

⇒ (12)

^{2}= OP^{2}+^{ }PQ^{2}⇒ (12)

^{2 }= 5^{2}+ PQ^{2}
⇒PQ

^{2}= 144 - 25
⇒PQ

^{2}= 119
⇒PQ = √119 cm

(D) is the correct option.

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.

**Answer**

AB and XY are two parallel lines where AB is the tangent to the circle at point C while XY is the secant to the circle.

_{}

^{}

_{}

^{}

_{}

^{}