Question

In the figure, PA and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to scale.

Answer 1

48

Explanation:

Since PD bisects BPA, we can say angle AOC and BOC are equal. So Angle BOC = 42.

Since PB is tangent to the circle, PBO is 90 degrees (tangent means 90 degrees at point of tangency).

Now looking at triangle PBO (also, 3 angles of a triangle add up to 180), we can say:

BPO + PBO + BOC = 180

BPO + 90 + 42 = 180

BPO + 132 = 180

BPO = 180 - 32 = 48

Option c is right.