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Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 669.
Sice D is midpoint of arc AB and I is incenter of triangle ABC we have C, I, D are collinear. Similarly A, I, E are collinear. Then by Pascal's theorem for A, F, C, E, B and D we have G, I, H are collinear.
This problem admits an extension:Replace I by any point in the internal region of tr ABC; let X and Y be the touching points of lines AI and BI with the circle. Keep definitions of F, G and H like the original problem. The colineality is still true!