Geometry Problem 1264

Elements: Triangle, Exterior Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines

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). Line DFG is perpendicular to BC (F on BC extended, G and G1 on arc AC). If BH is perpendicular to AG, prove that lines BH, EG, and AC are concurrent. Similarly for G1.


Geometry Problem 1264: Triangle, Exterior Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines