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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 = 30o
since Δ APO ≈ ΔBPO
∠APO = ∠BPO = 30o
∴∠APB = 60o
ΔAPB is equilateral
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