The figure below shows a circle of radius r,
chords AB and CD are parallel, chords BC and DE parallel. If
angle ABC = 45 degrees, AB = a, BC = b, CD = c, and DE = d,
prove that a2 + c2 = b2 + d2 = 4r2.
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."