NCERT Solutions class 10 maths chapter 10

Circles

NCERT Solutions class 10 maths chapter 10 Exercise 10.1

Question 1

How many tangents can a circle have?

Answer:

There can be infinit 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 …………

Answer:

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

(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 the 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) √119 cm

Answer:

In ΔOPQ

OQ² = OP²+PQ²

(12)² = 5²+PQ²

PQ² = 144-25

PQ² = 119

PQ = √119 cm

So, option D is correct

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.

Answer:

Let AB be line such that
AB∥CD∥EF.
CD is a secant , EF is a tangent intersecting the circle at H.