Online Geometry Problem 714: Triangle, Parallel, Cevians, Midpoints, Median, Ceva Theorem. Level: High School, Honors Geometry, College, Math Education

The figure shows a triangle ABC with DE
parallel to AC. AE and CD meet at F. BF meets DE and AC at H and G,
respectively. Prove that G is the midpoint of AC and H is the midpoint
of DE.