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Problem 586: Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters,
Circumcircles, Concurrency. Level: Mathematics Education, High School, College
The figure shows a cyclic quadrilateral ABCD
with circumcenter O.
Diagonals AC and BD meet at M. Let P be any point inside or outside the
circle O. If E, F, G, and H are the circumcenters of
triangles APB, BPC, CPD, and APD, respectively, prove that lines EG, FH,
and MO are concurrent at the same point Q.
