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    Question

    "In the given figure, 'O' is the center of the circle.

    If XR = 24 cm and RS = 18 cm, find the length of XO."
    A 5.5 cm Correct Answer Incorrect Answer
    B 7.5 cm Correct Answer Incorrect Answer
    C 7 cm Correct Answer Incorrect Answer
    D 5 cm Correct Answer Incorrect Answer

    Solution

    ATQ, RS × RZ = RX2  (Tangent secant Theorem) Let SZ = 'a' cm So, RS × (RS + a) = RX2 Or, 18 × (18 + a) = 242 Or, (18 + a) = 576 ÷ 18 Or, 18 + a = 32 Or, a = 14 So, SZ = 14 cm Since, O is the centre of the circle, SZ is the diameter. So, radius of the circle = 14 ÷ 2 = 7 cm So, XO = 7 cm

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