Question

Two tangent segments PA and PB are drawn to a circle with center O such that ∠APB = 120°. Prove that OP = 2AP

Answer 1

A + P

OP bisects ∠APB

∠APO = ∠OPB =`1/2`∠𝐴𝑃𝐵 =`1/2`× 120° = 60°

At point A

OA ⊥ AP, ∠OAP = 90°

In ΔPDA, cos 60° = `(AP)/(DP)`

`1/2=(AP)/(DP)`⇒ O𝑃 = 2𝐴𝑃