The figure below shows a triangle ABC with
the incircle O tangent to AB, BC, and AC at E, F, and D, respectively.
GH is parallel to AC and tangent to the circle O.If AE = 7, EG = 1, and
FH = 2, find CF.
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."