Nikolaos Dergiades, Francisco Javier García Capitán, and Sung Hyun Lim,
On six circumcenters and their concyclicity,
Forum Geometricorum, 11 (2011) 269--275.

Abstract.   Given triangle ABC, let P be a point with circumcevian triangle A'B'C'. We determine the positions of P such that the circumcenters of the six circles PBC', PB'C, PCA', PC'A, PAB', PA'B are concyclic. There are two such real points P which lie on the Euler line of ABC provided the triangle is acute-angled. We provide two simple constructions of such points.

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