Question

Two circles with centres p and q intersect at b andc. a, d are points on the circles with centres p and q respectively such that a, c, d are collinear. if ∠apb = 130°, and ∠bqd = x°, then the value of x is

Answer 1

Draw the diagram as per the question.
Join BC.
<BQD = Angle at the center of the circle standing on the arc BD
<BCD = Angle at the circumference of the circle standing on the arc BD
=> <BCD = (1/2) <BQD = x/2 --------- (1)
<ACB = Angle at the circumference of the circle standing on arc AB
<APB (reflex) = Angle at the center of the circle standing on the arc AB
=> <ACB = (1/2) Reflex <APB = (1/2)(360 - 130) deg = 115 deg
<BCD = 180 - <ACB = 180 - 115 = 65 deg ------ (2)
From (1) and (2) we get <BCD = x/2 = 65 deg
=> x = 130 deg