Online Geometry
Problem 660: Triangle, Circle, Diameter, Perpendicular
Lines. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows a triangle ABC. The circle
with diameter AC meet BC and BA extended at D and E, respectively. DF
and EG are perpendicular to AC. If GD and EF meet at H, prove that HB is
perpendicular to AC. See also:
Art of Problem 660 using Mobile Apps