Question

Prove that the tangent at the end of the chord make equal angle

Answer 1

Let PQ be the chord of a circle with center O Let AP and AQ be the tangents at points P and Q respectively. Let us assume that both the tangents meet at point A. Join points O, P. Let OA meets PQ at R Here we have to prove that ∠APR = ∠AQR Consider, ΔAPR and ΔAQR AP = AQ [Tangents drawn from an internal point to a circle are equal] ∠PAR = ∠QAR AR = AR [Common side] ∴ ΔAPR ≅ ΔAQR [SAS congruence criterion] Hence ∠APR = ∠AQR [CPCT]