Question

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

Answer 1

Given: AP and BP are tangents of circle having centre O.

To Prove: AP = BP

Construction: Join OP, AO and BO

Proof: ∠OAP and ∠OBP

OA = OB   ...[Radius of circle]

OP = OP   ...[Common side]

OAP = OBP = 90°   ...(Radius – tangent angle)

ΔOAP ≅ ΔOBP   ...[RHS congruency rule]

AP = BP   ...[CPCT]

Hence Proved.