The figure below shows a semicircle of
diameter CD tangent to AB and AE at G and F, respectively, so
that angle A = angle B = angle E = 90 degrees. If AF = a, FE
= b, and DG = x, prove that x2 = 2a(a+b).
Geometry problem solving is one of the
most challenging skills for students to learn. When a problem
requires auxiliary construction, the difficulty of the problem
increases drastically, perhaps because deciding which
construction to make is an ill-structured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."