The figure below shows a circumscribed
trapezoid ABCD (AD // BC) with BC, CD, AD, and AB tangent to the
inscribed circle at points E, F, G, and H. DE and CG intersect at K. If
CE = 2 and DG = 5, find KF.
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."