## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 3 of Exercise 12B

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

3
##### In the given figure, O is the center of a circle. PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70°, find ∠TRQ.

Given: In the figure, PT and PQ are two tangents and TPQ = 70°

To Find: TRQ

Construction: Join OT and OQ

In quadrilateral OTPQ

OTP = 90°

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

OQP = 90°

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

TPQ = 70° [Common]

By Angle sum of Quadrilaterals,

In quadrilateral OTPQ we have

OTP + OQP + TPQ + TOQ = 360°

90° + 90° + 70° + TOQ = 360°

250° + TOQ = 360

TQO = 110°

Now,

As we Know the angle subtended by an arc at the center is double the angle subtended by it at any

point on the remaining part of the circle.

we have

TOQ = 2TRQ

110° = 2 TRQ

TRQ = 55°

1
2
3
4
5
6
7
8
9
10
11
12
13
14