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

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

Given: A circle with centre O and PQ, PR are tangents to the circle from an external point P.

To Prove: PQ = PR

Construction: Join OP, OQ, OR

Proof: In ΔOPQ and ΔOPR

OP = OP (common)

OQ = OR (radii of the same circle)

∠OQP = ∠ORP (each 90^°)

ΔPOQ ≅ ΔPOR (RHS congruence)

PQ = PR