The figure below shows a triangle ABC with cevians AD and CE meeting at F. If angle ACB = 30 degrees,
angle BAD = 8 degrees, angle DAC = 86 degrees, and angle BED = 92
degrees, find the measure of angle AFC.
Try to solve this problem using elementary geometry (Euclid's
Elements, no trigonometry).
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.