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    Question

    The internal bisector of ∆ABC at ∠A cuts BC on D and

    cuts the circum circle at E if DE = 6cm, AC = 8cm and AD = 10 cm then find the length of AB?
    A 32 cm Correct Answer Incorrect Answer
    B 15 cm Correct Answer Incorrect Answer
    C 18 cm Correct Answer Incorrect Answer
    D 20 cm Correct Answer Incorrect Answer

    Solution

    From the diagram, AE = AD + DE  AE = 10 + 6 = 16 cm  ∠ABC = ∠CED  In ∆ADB and ∆AEC, (AB)/(AE ) = (AD)/(AC)                     (due to Similar triangle) (AB)/(16) = (10)/(8)      AB = 20 cm 

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