Geometry Problem 1366: Square, Angle Bisector, Perpendicular, Concyclic Points, Circle, Sketch, iPad Apps.

Proposition

In the figure below, ABCD is a square and E is any point on AD. The bisector of angle EBC meets CD at F. FG is perpendicular to BE (G on BE), AG and BF extended meet at H. Prove that the points A, B, C, H, and D are concyclic (they lie on a common circle).
 

See solution below

 

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Sketch and Typography of problem 1366 using iPad Apps

See solution below

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