(a) In the figure given below, two circles intersect at points P and Q. If ∠A = 80° and ∠D = 84°, calculate

(i) ∠QBC

(ii) ∠BCP

Solution:

1. (i) ABCD is a cyclic quadrilateral

∠A + ∠C = 180^o

30^o + p = 180^o

P=180^o – 30^o = 150^o

(ii) Arc BD subtends ∠BOD at the center

And ∠BAD at the remaining part of the circle

∠BOD = 2 ∠BAD

q = 2 × 30^o = 60^o

∠BAD = ∠BED are in the same segment of the circle

∠BAD = ∠BED

30^o = r

r = 30^o

1. Join PQ

AQPD is a cyclic quadrilateral

∠A + ∠QPD = 180^o