Problem 315: Three tangent
circles, Common external tangent line, Geometric Mean
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The figure shows circles A (radius a), B (radius b),
and C (radius c) tangent to both sides of an angle D. Circles A
and B are tangent at the point E, and circles B and C are
tangent at the point F. Prove that b is
the geometric mean of a and c.
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a
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