The figure below shows a square ABCD of side
"a" and the square AGHM. The circle O of radius OH = GH/2 is
tangent to BC, CD and EF. Prove that .
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.