Question

In the given figure, A and B are the centres of two intersecting circles and PQ is their common chord. angle APB=70^ and angle PAQ=80^ . Find the measure of angle PBQ​

Answer 1

Answer:

NCERT

Theorem 10.1 : Equal chords of a circle subtend equal angles at the centre. Proof : You are given two equal chords AB and CD of a circle with centre O (see

Answer 2

Option c is correct

in triangle APQ

angle PAQ = 80 °

AP = AQ ( radius)

so angle angle APQ AND AQP are equal

angle PAQ + APQ + PQA = 180 ( angle sum property)

80° + x + x = 180

80 + 2x = 180

2x = 180 - 80

2x = 100

x = 100÷2

x = 50

In triangle PBQ

angle BPQ = Angle APB - angle apq

angle BPQ = 70 - 50

angle BPQ = 20

DUE TO B IS CENTRE OF CIRCLE

SO BP = BQ ( RADIUS OF CIRCLE )

SO ANGLE BPQ = BQP

angle BPQ + angle PQB + angle QBP = 180

20 + 20 + angle QBP = 180

40 + angle QBp = 180

QBP = 180 - 40

QBP = 140