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