Math: Geometry Problem 1002:
Triangle, Circle, Circumcircle, Cevian, Parallel Lines, Cyclic
Quadrilateral, Concyclic Points. Level: School, College.
The figure below shows a triangle ABC
with D and E on AC. EF is parallel to BC (F on circumcircle of
triangle ABD) and EG is parallel to AB (G on circumcircle of
triangle BCD). Prove that points D, E, G, and F are concyclic.