NCERT Solutions for Class 10 Maths Chapter 10 Circles Ex 10.2

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 1

Solution for Ex 10.2 Class 10 Maths Question 1
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 2

Solution for Ex 10.2 Class 10 Maths Question 2
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 3

Solution for Ex 10.2 Class 10 Maths Question 3
 

Ex 10.2 Class 10 Maths Question 4.

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

Solution for Ex 10.2 Class 10 Maths Question 4

Solution for Ex 10.2 Class 10 Maths Question 4
 

Ex 10.2 Class 10 Maths Question 5.

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

Solution for Ex 10.2 Class 10 Maths Question 5

Solution for Ex 10.2 Class 10 Maths Question 5
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 6

Solution for Ex 10.2 Class 10 Maths Question 6
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 7

Solution for Ex 10.2 Class 10 Maths Question 7
 

Ex 10.2 Class 10 Maths Question 8.

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

Solution for Ex 10.2 Class 10 Maths Question 8

Solution for Ex 10.2 Class 10 Maths Question 8
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 9

Solution for Ex 10.2 Class 10 Maths Question 9
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 10

Solution for Ex 10.2 Class 10 Maths Question 10
 

Ex 10.2 Class 10 Maths Question 11.

Prove that the parallelogram circumscribing a circle is a rhombus.

Solution for Ex 10.2 Class 10 Maths Question 11

Solution for Ex 10.2 Class 10 Maths Question 11
 

Ex 10.2 Class 10 Maths 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 for Ex 10.2 Class 10 Maths Question 12

Solution for Ex 10.2 Class 10 Maths Question 12
 

Ex 10.2 Class 10 Maths Question 13.

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

Solution for Ex 10.2 Class 10 Maths Question 13

Solution for Ex 10.2 Class 10 Maths Question 13
 

 

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