The figure below shows a circle O with
radius OB perpendicular to radius OA. CD is perpendicular to OA (C on
circle O, D on OA). OC and BD extended meet at E. Circle of radius OE
meets OA extended at F. EG is perpendicular to OF (G on OF). Prove that
AF = EG.
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."
