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If two tangents are drawn to a circle from an external point, show that they subtend equal angles at the center.
Let PT and PQ are two tangents from external point P to a circle with center O
To Prove : PT and PQ subtends equal angles at center i.e. ∠POT = ∠QOT
In △OPT and △OQT
OP = OQ [radii of same circle]
OT = OT [common]
PT = PQ [Tangents drawn from an external point are equal]
△OPT ≅ △OQT [By Side - Side - Side Criterion]
∠POT = ∠QOT [Corresponding parts of congruent triangles are congruent]