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    Question

    The radii of two concentric circles are 20 cm and 25 cm.

    A straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 32 cm, then the length (in cm.) of PS is:(Approx.)
    A 40cm Correct Answer Incorrect Answer
    B 42cm Correct Answer Incorrect Answer
    C 43.8cm Correct Answer Incorrect Answer
    D 46cm Correct Answer Incorrect Answer

    Solution

    In the right triangle OQM. OM = √ (20²- 16²) = √144 = 12cm In the right triangle OMS. Let RS = x cm So, (25) ² = (12) ² + (x + 16) ² (x + 16) ² = 625 – 144 = 481 x + 16 = 21.9 x=21.9 - 16 =5.9 x = 5.9 So, PS = 2 × (16 + 5.9) = 43.8 cm

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