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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.
 
 

Right triangle, Incircle, Excircle, Collinear tangency points
 
 
 

 

 

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