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 ill-structured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."