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Let A, B, and C be collinear and let P be a point not on the line ABC. Then P and the circumcenters of APB, BPC, and APC are concyclic.

See problem 5.86 in V. Prasolov, Problems in Plane and Solid Geometry, Vol. 1, Plane Geometry [PDF], (D. Leites, ed. and trans.).

Contributed by: Jay Warendorff

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Three Circumcenters Concyclic with a Fourth Point