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