Geometry Problem 1268

Elements: Triangle, Exterior Angle Bisector, Circumcircle, Circle, Chord, Parallel, Concyclic Points, Cyclic Quadrilateral

In the figure below, ABC is a triangle inscribed in a circle O. Line EBD is the exterior bisector of the angle ABC (D on AC extended, E on arc AB). A chord EG cuts AC at X. BC extended meets GD at F. BX extended meets AG at H. Prove that (1) HF and AD are parallel; (2) Points B, F, G, and H are concyclic.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.


Geometry Problem 1268: Exterior Angle Bisector, Circumcircle, Circle, Chord, Parallel, Concyclic Points, Cyclic Quadrilateral

See also:
Geometry problem 1268 in motion.