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Problem 482: Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points

The figure shows a triangle ABC with circumcircle C1, incenter D, and excenter E corresponding to BC. If F is the midpoint of arc BC, prove that points D, B, E, and C lie on a circle with center at F.
 Circumcircle of a triangle is the circle which passes through the vertices. Incenter is the center of the incircle. Excenter is the center of an excircle.

 

Triangle, Circle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic