# A Cyclic Quadrilateral Concurrency

A Cyclic Quadrilateral Concurrency

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.

O

1

O

2

O

3

O

4

OO

1

3

OO

2

4

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