Online Geometry Problem 706: Triangle, Cevian, Three Circumcenters,
Circumcircles, Concyclic Points.
Level: High School, Honors Geometry, College,
In a triangle ABC, O is the circumcenter,
and D is a point on AC. If E and F are the circumcenters of triangles
ABD and BDC, respectively, prove that the points B, E, O, and F are
concyclic. (See the figure below.)