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

Given :PT and TQ are two tangents drawn from an external point T to the circle C(o,r)
To prove :PT=TQ
Proof : We know that a tangent to the circle is ⊥ to the radius through the point of contact. So,∠OPT=∠OQT, OT=OT(common)∠OPT=∠OQT=90°(Tangent and radius are perpendicular at point of contact)
OP=OQ=radius
∴ΔOPT≅ΔOQT(RHS congruence)
∴PT=TQ(by c.p.c.t)
So, length of the tangents drawn from an external point to circle are equal.