NCERT Solutions for Class 10 Maths Chapter 10 – Circles

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) 12 cm
(B) 13 cm
(C) 8.5 cm 
(D) √119 cm

Answer

The line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴ OP ⊥ PQ

By Pythagoras theorem in ΔOPQ,

OQ² = OP² + PQ²
⇒ (12)² = 5² + PQ²

⇒PQ² = 144 - 25

⇒PQ² = 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.