The figure below shows a triangle ABC
with the incenter I, a cevian BD, the circumcircle O and M midpoint of arc
AC. A line segment through I and perpendicular to the bisector of the
angle BDC intersects BD at E, and AC at F. MF extended intersects arc BC
at T. Prove that the circumcircle Q of the triangle EFT is tangent to BD
at E, AC at F, and arc BC at T.
See also: Typography and poster of problem 1408.