Tangets from external point to the circle are equal
Prove that the length of the tangents drawn from an external point to a circle are equal. . Answer: Given : Let AP and BP be the two tangents drawn from external point P to the circle with centre O. To Prove : AP = BP Proof : In Δ AOP and Δ BOP OA = OB (radii) ∠ O A P = ∠ O B P = 90 ∘ (Line drawn from from center to the tangent through the point of contact is perpendicular) OP = OP (common) ∴ Δ A O P ≅ Δ B O P (R.H.S.) ∴ AP = BP ( C P C T ) Therefore the length of the tangents drawn from an external point to a circle are equal.