Geometry Problem 1411: Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle

Proposition

The figure below shows a right triangle ABC (angle B = 90 degree) with the incircle I tangent to BC at D. The excircle E corresponding to BC is tangent to BC and tangent to the extensions of AB and AC at F, G, and H, respectively. The extensions of GD and FH meet at J. Prove that the triangle GJH is an isosceles right triangle.
 
 
 

Geometry Problem 1411: Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle, 45 Degree Angle, Tutor
 
 


Poster of Problem 1411: Sketching, iPad, Typography, Art

Poster of Geometry Problem 1411: Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Sketching, iPad, Typography, Art, SW, Tutor

 

See also: Typography and poster of problem 1408.