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    Question

    Two chords, AB and CD, of a circle intersect at an external

    point E. Given that the lengths of BE and DE are 12 cm and 8 cm, respectively, and the total length of chord AB is 36 cm, determine the length of chord CD.
    A 64 cm Correct Answer Incorrect Answer
    B 80 cm Correct Answer Incorrect Answer
    C 48 cm Correct Answer Incorrect Answer
    D 72 cm Correct Answer Incorrect Answer

    Solution

    BE = 12 cm, DE = 8 cm, and AB = 36 cm

    Image
    From the secant theorem:

    AE X BE = CE X DE .... (I)

    AE = AB + BE = 36 + 12 = 48 cm

    Put the value of AE in equation (I) , we get,

    48 X 12 = CE X 8

    Or, CE = 48 X 12 X (1/8)

    So, CE = 72 cm

    Therefore, the length of the chord CD = CE - DE = 72 - 8 = 64 cm

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