It is proved that the intersection point d is parallel to BF and intersects AC at point H.

In the triangle ADH, AE=ED= 1/2AD, EF//DH.

So AF=FH= 1/2AH.

In the triangular BCF, BD=DC= 1/2BC, BF//DH.

So CH=FH= 1/2FC.

To sum up, AF=FH=FC= 1/2FC.

Hope to adopt