Problem 347. Triangle, Altitude, Perpendicular, Circle, Concyclic points.
Level: High School, College, SAT Prep.
The figure shows a triangle ABC with
the altitude BD. DE is perpendicular to AB and DF is
perpendicular to BC. Prove that the points A, E, F, and C are
concyclic (lie on a same circle).
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."