Proposition

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

 

 

See solution below

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Geometric Art: Poster of problem 1413

See solution below

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Geometric Art: Hyperbolic Kaleidoscope of problem 1413 using iPad Apps

 

See also: Typography and poster of problem 1408.