In the diagram below, the circles A and B intersect at C and
D. CE is tangent to circle A at C, CF is tangent to circle B at C,
circle G passes through the points C, E, F. If HM is tangent to circle G
at C, prove that C is the midpoint of HM.
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 illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
