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    Question

    In a circle with center O and radius 10 cm, two chords

    AB and CD are parallel and 6 cm apart. If the length of chord AB is 16 cm, what is the length of chord CD?
    A 12 cm Correct Answer Incorrect Answer
    B 16 cm Correct Answer Incorrect Answer
    C 15 cm Correct Answer Incorrect Answer
    D 18 cm Correct Answer Incorrect Answer

    Solution

    For chord AB, the perpendicular distance from O to AB divides it into two equal halves of 8 cm each. Using Pythagoras in the triangle formed,  the perpendicular distance from O to AB = sqrt(10²  - 8² )  = sqrt(100 - 64) = sqrt(36) = 6 cm. The chords AB and CD are equidistant from the center, so chord CD is also divided into two equal halves. Length of chord CD = 2 * sqrt(10²  - 6² )  = 2 * sqrt(100 - 36) = 2 * sqrt(64)  = 16 cm. Correct answer: b) 16 cm

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