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Online Geometry Problem 448: Tangent Circles, Diameter, Perpendicular, Chord

The figure shows a circle O of diameter AB and a circle O' tangent at C and D to AB and circle O, respectively. DF is perpendicular to AB. Lines DF and EC meet at G. If AC=a, DG=b, and CD=x, prove that x2=a.b.

Tangent circles, common chord, diamter 


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