Q30 of 52 Page 10

Prove that the lengths of two tangents drawn from an external point to a circle are equal. (CBSE 2013,2014,2015,2016,2017,2018)


Let us consider a circle with center O.


TP and TQ are two tangents from point T to the circle.


To Proof : PT = QT


OP ⏊ PT and OQ ⏊ QT [Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


∠OPT = ∠OQT = 90°


In △TOP and △QOT


∠OPT = ∠OQT [Both 90°]


OP = OQ [Common]


OT = OT [Radii of same circle]


△TOP ≅ △QOT [By Right Angle-Hypotenuse-Side criterion]


PT = QT [Corresponding parts of congruent triangles are congruent]


Hence Proved.

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