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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 тКе AC and BC тКе AC тИа DAE = тИа BCE = 90┬░ In тЦ│ DAE and тЦ│ BCE тИа DAE = тИа BCE = 90┬░ тИа AED = тИа BEC (Vertical angle) тЦ│ DAE ~ тЦ│ BCE (By AA similarity) By C.P.C.T = AE/EC = AD/BC = 12/18 = 8/BC ┬а BC = (18├Ч8)/12 =144/12 x= 12cm ┬а The correct answer is 12 cm.

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