Online Geometry Problems, High School, College

Geometry Problem 482: Co-Circularity of Incenter, Excenter, and Two Vertices in a Triangle Inscribed in Circumcircle

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 the center at F.
The circumcircle of a triangle is the circle that passes through the vertices. The incenter is the center of the incircle, and the excenter is the center of an excircle.".


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