The figure below shows a right triangle ABC (angle B = 90 degree)
with the altitude BH. The incircle I is tangent to BC at D. The excircle E corresponding to BC is
tangent to BC at G and tangent to the extension of AB at F. FD extended and BH meet at J. Prove that
the measure of the angle FJG is 45 degree.
See also: Typography and poster of problem 1408.