Question

Please help me. Only answer if you know the answer. In circle O, PA and PB are tangents. The figure is not drawn to scale.

a. Prove that APO is congruent to BPO.

b. Find BOD for AOP = 64. Explain your reasoning.

Answer 1

a. See down below

b. 116 degrees

Explanation:

a. Since PA and PB are both tangents to the circle, they both form right angles with the radius of the circle. Also, since they originate from a common point, they have equal length when they reach the circle. Finally, they share side PO. Therefore, by SSA congruence, they are congruent triangles.

b. Since PD bisects the circle, it is divided into two 180 degree sections. If AOP=64, then so is POB. Since all of the remaining half of the circle is BOD, you can find its angle measure by subtracting the angle measure of AOP from 180. 180-64=116 degrees. Hope this helps!