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:
a^{2/3} + b^{2/3} = x^{2/3}.
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