The figure shows a triangle ABC with
circumcircle C_{1}, 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.
