Problem 270. Tangent Circles, Common external tangent, Fractional exponents

In the figure below, A and B are tangent circles of diameters FC and CG respectively. If DE is the common external tangent, FD = a, EG = b, and FG = x, prove that: a2/3 + b2/3 = x2/3. View or post a solution.
 

Tangent circles and common external tangent
 

 

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