A Cyclic Quadrilateral Concurrency

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Let ABCD be a cyclic quadrilateral with circumcenter O. Let the diagonals AC and BD intersect at E. Let P be a point inside the quadrilateral and let , , , be the circumcenters of ABP, BCP, CDP and DAP. Then , , and OE are concurrent.


Drag the purple points A, B, C, or D to change the figure.


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


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