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]

Hence, Proved.