# 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

TOP QOT

[By Right Angle - Hypotenuse - Side criterion]

PT = QT

[Corresponding parts of congruent triangles are congruent]

Hence Proved.

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