Drawn to a circle with center o, Mathematics

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From a point P, two tangents PA are drawn to a circle with center O.If OP=diameter of the circle show that triangle APB is equilateral.

Ans: PA=PB (length of tangents from an external point

From ΔOAP,

sin∠APO =OA/OP = 1/2

Since OP = 2OA (Since OP=Diameter)

∴∠APO = 30^o

since Δ APO ≈ ΔBPO

∠APO = ∠BPO = 30^o

∴∠APB = 60^o

ΔAPB is equilateral

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