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    Question

    Two chords AB and CD of a circle intersect at a point F

    outside the circle. If AF = 12 cm, BF = 4 cm, and CF = 16 cm, find the length of CD.
    A 13 cm Correct Answer Incorrect Answer
    B 12 cm Correct Answer Incorrect Answer
    C 11 cm Correct Answer Incorrect Answer
    D 10 cm Correct Answer Incorrect Answer

    Solution

    AB =AF-BF =12-4=8 AB=8 If two chords AB and CD of a circle are cut at a point F outside the circle then,  AF × BF = CF × DF Let DF be a cm. So, according to the concept, AF × BF = CF × DF 12 × 4 = 16 × a  48 = 16a  a = 48/16  a = 3 So, DF = 3 Now, CD = CF - DF CD = 16 - 3 CD = 13 cm

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