Problem 567: Right triangle, Incircle, Excircle, Collinear tangency
points.
Level: High School, College, Math Education.
The drawing shows a right triangle ABC. The incircle D is
tangent to AB and AC at G and H, respectively. The excircle E is
tangent to CB extended at F. Prove that F, G, and H are
collinear points.

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