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).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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