The figure below shows a right triangle ABC (angle B = 90 degree)
with the altitude BH. The incircle I is tangent to AB, BC, and AC at D, F, and
H, respectively. The excircle E corresponding to BC is
tangent to BC at G. DG and BH meet at J. Prove that the
triangle JBF is an isosceles triangle (BJ = BF).
See also: Typography and poster of problem 1408.