The figure below shows a triangle ABC with the altitudes AH,
BK, and CJ. O_{1}, O_{2}, O_{3}, and O_{4} are
the centers of the squares ABDE, BCFG, AJJ_{1}J_{2}, and CHH_{1}H_{2}, respectively. M
is the midpoint of AC. Prove that the points O_{1}, O_{2}, O_{3}, O_{4}, M, and K are concyclic.