Home Geometry Problems All Problems 341-350 View or post a solution 
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).

Triangle, Altitude, Perpendicular, Concyclic points 



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."

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