Q. 13

If two tangents are drawn to a circle from an external point, show that they subtend equal angles at the center.

Answer :


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]


Hence, Proved.


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