Prove that the lengths of two tangents drawn from an external point to a circle are equal.

Let us consider a circle with center O.


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


To Proof : PT = QT


Proof :


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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