According to the question,
BD=CD and OD=DX
Therefore, BC and OX bisect each other and OBXC is a parallelogram.
This gives BX∥CO and CX∥BO
or BX∥CF and CX∥BE
or BX∥OF and CX∥OE
In ΔABX, as BX∥OF, then,
AOAX=AFAB .............(1)
In ΔACX, as CX∥OE, then,
AOAX=AEAC ............. (2)
From equation (1) and (2),
AFAB=AEAC
Hence, as E and F divides AB and AC respectively in the same ratio, so, FE∥BC.