## NCERT Solutions for Class 10 Maths Exercise 10.1 Chapter 10 Circles – FREE PDF Download

NCERT Class 10 Maths Ch 10 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths

Chapter 10 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Circles solutions will help you understand the chapter thoroughly.

# NCERT Solutions for Class 10 Maths Chapter 10 – Circles

1. How many tangents can a circle have?

**Ans.**A circle can have infinitely many tangents since there are infinitely many points on the circumference of the circle and at each point of it, it has a unique tangent.

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 _________.

**Ans.**(i) A tangent to a circle intersects it in

__exactly one__point.

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

__secant__.

(iii) A circle can have

__two__parallel tangents at the most.

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

__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) 12 cm (B) 13 cm (C) 8.5 cm (D) cm

**Ans.**(D) PQ is the tangent and OP is the radius through the point of contact.

OPQ = [The tangent at any point of a circle is to the radius through the point of contact]

In right triangle OPQ,

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

= 144 – 25 = 119

PQ = cm

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.

**Ans.**