In the following figure, P and Q are centres of two circles. The circles are intersecting at points A and B. PA produced on bot the sides meets the circles at C and D. If ∠CPB = 100°, then find the value of x.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 100
Given:
∠CPB = 100°
Calculations:
According to the figure:
∠APB + ∠CPB = 180º (∠APB is the supplementary angle of ∠CPB)
Now in triangle APB,
∠PAB = ∠PBA (AP = PB = radius)
∠ PAB = 50º
∠DAB = 180º - ∠PAB = 130º (Supplementary angle of ∠PAB)
In cyclic quadrilateral ABRD
∠BRD = 180º - 130º = 50º
According to the concept of the angle subtended by an arc at the centre is twice the angle subtended by it anywhere on the circle circumference.
∠BQD = x = 2 × 50º = 100º