Two tangent segments PA and PB are drawn to a circle with centre O, such that angle APB= 120degree. Prove that OP=2AP.
Given: O is the centre of the circle. PA and PB are tangents drawn to a circle and ∠APB = 120°.
To prove: OP = 2AP
In ΔOAP and ΔOBP,
OP = OP (Common)
∠OAP = ∠OBP (90°) (Radius is perpendicular to the tangent at the point of contact)
OA = OB (Radius of the circle)
∴ ΔOAP ΔOBP (RHS congruence criterion)
⇒ OP = 2 AP