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    Question

    In a circle, the chord AB is 12 cm, and the

    perpendicular from the center O to the chord AB bisects it at point P. If OP = 5 cm, what is the radius of the circle?
    A 6.5 cm Correct Answer Incorrect Answer
    B 7.8 cm Correct Answer Incorrect Answer
    C 8.6 cm Correct Answer Incorrect Answer
    D 10 cm Correct Answer Incorrect Answer

    Solution

    In the right-angled triangle OAP, OP = 5 cm and AP = 6 cm (since P bisects AB, so AP = AB/2 = 12/2 = 6 cm). Using the Pythagorean theorem: OA² = OP² + AP²  OA² = 5² + 6²  = 25 + 36 = 61  OA = √61. Thus, the radius of the circle is √61, which is approximately 7.81 cm. Correct answer: b.

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