The figure below shows a triangle ABC
with D and E on BC and F on AC so that BD = AF = FE = EC and
angle BAD = 2 angle DAE = 2 angle EAC. Prove that (1) FD // AB,
(2) B is the circumcenter of triangle AEF.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka.
Geometry art of problem 1161