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 x^{2}=a.b.