Join BX and CX
We have,
BD = CD and OD = DX
Thus, BC and OX bisect each other.
⇒ OB XC is a parallelogram.
⇒ BX II CO and CX II BO
⇒ BX II CF and CX II BE
⇒ BX II OF and CX II OE
In △ABX, we have
BX II OF
⇒ AOAX = AFAB ..... (i)
In △ACX, we have
CX II OE
⇒ AOAX = AEAC
From equations (i), (ii), we get
AFAB = AEAC
Thus, E and F are points on AB and AC such that they divide AB and AC respectively in the same ratio.
Therefore, by the converse of Thale's Theorem FE || BC.