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
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
OP = OQ
OT = OT
[Radii of same circle]
△TOP ≅ △QOT
[By Right Angle - Hypotenuse - Side criterion]
PT = QT
[Corresponding parts of congruent triangles are congruent]