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    Question

    In the given figure, Ab = 30 cm and CD = 24 cm. What is

    the value (in cm) of MN?
    A 18 Correct Answer Incorrect Answer
    B 9 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 15 Correct Answer Incorrect Answer

    Solution

    If we draw a perpendicular to a chord of any circle, the per divide the chord in two equal part. CD is chord for small circle and AB is chord for bigger circle.   r = small circle radius   R = bigger circle radius Apply PGT in ∆ OTC x2 = (x)2 – (12)2 ---- (1) Apply PGT in ∆ OAP x2 = (R)2 – (15)2 ------(2) From   (1) and (2) R2 – (15)2 = r2 – (12)2 R2 – r2 = 225 – 114 = 81 Apply PGT in ∆ OTM R2 – r2 = TM2 81 = TM2 TM = 9 We know OT divide chord MN in 2 equal part (TM = TN) MN = TM + TN MN = 9 + 9 = 18

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