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    Question

    Two circles with centers B and D have radii DA = 8 cm

    and BC = x cm, respectively. AC is tangent to both circles. If DB and AC intersect the point E, AE = 12 cm, and EC = 18 cm, then find the value of x (in cm).
    A 12 Correct Answer Incorrect Answer
    B 18 Correct Answer Incorrect Answer
    C 21 Correct Answer Incorrect Answer
    D 16 Correct Answer Incorrect Answer

    Solution

    AD ⊥ AC and BC ⊥ AC ∠ DAE = ∠ BCE = 90° In △ DAE and △ BCE ∠ DAE = ∠ BCE = 90° ∠ AED = ∠ BEC (Vertical angle) △ DAE ~ △ BCE (By AA similarity) By C.P.C.T = AE/EC = AD/BC = 12/18 = 8/BC   BC = (18×8)/12 =144/12 x= 12cm   The correct answer is 12 cm.

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