Online Geometry Problem 812: Four Tangent Circles, Common Tangent Line, Diameter, Area, Collinear Centers. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows the tangent circles of diameters AB, BC, CD, and AD so that the line EFG is the common tangent to circles AB, BC, and CD at E, F, and G, respectively. If EF = a and FG = b, prove that the shaded area .