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Four Concyclic Points

Let ABC be a triangle and H the foot of the altitude from B. Let M be the midpoint of AC. Let P and Q be the feet of the perpendiculars from A and C to the angle bisector of the angle ABC. Then H, M, P and Q lie on a circle.

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D. Grinberg, "From Baltic Way to Feuerbach: A Geometrical Excursion," Mathematical Refections [online] (2), 2000 p. 2.

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"Four Concyclic Points" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/FourConcyclicPoints/
Contributed by: Jay Warendorff
After work by: D. Grinberg




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