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IL LaPPy 2 marks each.Prove that the tangents at the extermities of any chord make equal angles withthe chord. |
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Answer» 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 Join points O, P. Let OA meets PQ at R.Here we have to prove that ∠APR = ∠AQRConsider, ΔAPR and ΔAQRAP = AQ [Tangents drawn from an internal point to a circle are equal]∠PAR = ∠QARAR = AR [Common side]∴ ΔAPR ≅ ΔAQR [SAS congruence criterion]Hence ∠APR = ∠AQR [CPCT] |
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