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    Question

    In a circle of radius 5 cm, a point P lies outside the

    circle at a distance 13 cm from the centre O. Tangents PA and PB are drawn from P to the circle, touching at A and B. Find the length of chord AB.
    A 110/13 cm Correct Answer Incorrect Answer
    B 120/13 cm Correct Answer Incorrect Answer
    C 120/11 cm Correct Answer Incorrect Answer
    D 127/17 cm Correct Answer Incorrect Answer

    Solution

    OP = 13, OA = OB = 5 Right triangle OAP: AP┬▓ = OP┬▓ тИТ OA┬▓ = 13┬▓ тИТ 5┬▓ = 169 тИТ 25 = 144 тЗТ AP = 12 cm тИаOAP is angle between OP and AP. sinтИаOAP = opposite/hypotenuse = AP/OP = 12/13 Angle at centre subtended by chord AB is тИаAOB = 2тИаOAP. Chord length formula: AB = 2r sin(тИаAOB/2) = 2r sin(тИаOAP) So AB = 2 ├Ч 5 ├Ч (12/13) = 120/13 cm.

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