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    Question

    In a circle with center O, two tangents PA and PB are

    drawn from point P outside the circle. If PA = 24 cm, PB = 24 cm, and OP = 30 cm, find the length of chord AB.
    A 25 cm Correct Answer Incorrect Answer
    B 26 cm Correct Answer Incorrect Answer
    C 28 cm Correct Answer Incorrect Answer
    D 36 cm Correct Answer Incorrect Answer

    Solution

    In the right triangle OPA, OA = OP = 30 cm (radius of the circle). In right triangle OPA, by Pythagoras’ theorem, PA² = OP² - OA² 24² = 30² - OA² 576 = 900 - OA² OA² = 324 OA = 18 cm. The length of chord AB = 2 × OA = 36 cm.

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