Problem 358. Isosceles triangle 80-80-20, Circle, Angles, Congruence.
Level: High School, College, SAT Prep.
In the figure below, triangle ABC is
isosceles with AB = BC and angle B = 20°. The cevian AD is equal
to BD and the circle of center C and radius equal to CA cut AB
and BC at points E and F, respectively.
Geometry problem solving
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."