Online Geometry Problem 702: Triangle, Circumcircle, Parallel, Concyclic
Points.
Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows a triangle ABC with DE
parallel to AC. F is a point on BC and the circumcircle of triangle DEF
intersects AB at G. Prove that points A, G, F, and C are concyclic (lie
on a same circle).