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