Concyclic Points Related to a Midpoint and the Incircle

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Let ABC be a triangle and M be the midpoint of AB. Let A', B', and C' be the intersections of the incircle with BC, AC, and AB, respectively. Let γ be a circle that passes through A and B and contains A' and B' in its interior. Let A'B' intersect γ at P and Q. Then P, Q, C', and M are concyclic.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


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