Problem 270. Tangent Circles, Common external tangent, Fractional exponents
Problem 270: Triangle, Cevian, Incircle, Excircle, Inradius, Exradius, Congruence.
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.