Question

Prove that the tangents drawn at the end points of the chord makes equal angles with the chord

Answer 1

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Let AB be a chord of a circle with center O and let AP and BP be the tangents at A and B.Let the tangent meet at P.Join OP Suppose OP meets AB at C.To prove : ∠PAC = ∠PBCProof : In ΔPAC and ΔPBCPA = PB [Tangents from an external point to a circle are equal]∠APC = ∠BPC [PA and PB are equally inclined to OP]PC = PC [Common]ΔPAC ≅ ΔPBC [SAS Congruence]∠PAC = ∠PBC [C.P.C.T]

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