The figure shows a right triangle ABC,
D is on AC extended and E on AB extended, angle A = 2(angle
CBD), and angle BCE = 3(angle CBD). Prove that the points B, C,
D, and E are concyclic ((lie on a same circle).
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."
