Let BD be a median in triangle ABC. The points E and F divide the median BD in three equal parts, such that BE = EF = FD. If AB = 1 and AF = AD, find the length of the line segment CE.
I have tried few standard tools like using mass point geometry as well as Stewart's theorem but had no success. I do get a feel that I am not able to see something very obvious in this geometrical construct. Help is appreciated.
Indeed there is something really simple in this construct : given the lengths and angles, it can be shown that
$$\triangle AFB \cong \triangle CDE$$
by $SAS$ congruence. Using $\triangle AFD$ is isosceles, gives $\angle AFB=\angle CDE$.
Hence $CE=AB$ follows.