Geometry Problem 461: Three Circles, Tangent, Right Angle, Center, Distance, Measurement

The figure shows three circles of radii a, b, and c tangent at points D and E, and tangent to the sides of right angle FOG at points F, H, M, and G. If BC=x, prove that .
 

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Proposed Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement.

Proposed Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement.

Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.