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 also: Typography and poster of problem 1408.