# NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.2

Get Free NCERT Solutions for Class 10 Maths Chapter 10 Ex 10.2 PDF. Circles Class 10 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 10.2 Class 10 Maths NCERT Solutions were prepared by Experienced ncert-books.inTeachers. Detailed answers of all the questions in Chapter 10 Maths Class 10 Circles Exercise 10.2 provided in NCERT TextBook.

Question 1.

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

(a) 7 cm

(b) 12 cm

(c) 15 cm

(d) 24.5 cm

Solution:

Question 2.

In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

(a) 60°

(b) 70°

(c) 80°

(d) 90°

Solution:

Question 3.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to

(a) 50°

(b) 60°

(c) 70°

(d) 80°

Solution:

Question 4.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Solution:

Question 5.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Solution:

Question 6.

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Solution:

Question 7.

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Solution:

Question 8.

A quadrilateral ABCD is drawn to circumscribe a circle (see figure). Prove that AB + CD = AD + BC.

Solution:

Question 9.

In figure, XY and X’Y’ are two parallel tangents to a circle , x with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°.

Solution:

Question 10.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

Solution:

Question 11.

Prove that the parallelogram circumscribing a circle is a rhombus.

Solution:

Question 12.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see figure). Find the sides AB and AC.

Solution:

Question 13.

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Solution: