Prove that the lengths of the 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
Construction: Join OT.
Proof: We know that, a tangent to a circle is perpendicular to the radius through the point of contact.
Therefore, ∠OPT = ∠OQT = 90°
In ΔOPT and ΔOQT,
OT = OT (Common)
Radius of the circle = OP = OQ
∠OPT = ∠OQT = 90°
Therefore, ΔOPT ≅ ΔOQT (RHS congruence criterion)
Therefore, PT = TQ
So, the length of the tangents drawn from an external point to a circle are equal.