Given $\displaystyle \Delta ABC$ as shown with $\displaystyle AF=\frac{1}{4} AB$ , $\displaystyle AE=\frac{1}{4} AC$ and $\displaystyle \overline{BE} \cap \overline{CF}=0$ prove $\displaystyle AO$ hits $\displaystyle \overline{BC}$ at its midpoint.
Given $\displaystyle \Delta ABC$ as shown with $\displaystyle AF=\frac{1}{4} AB$ , $\displaystyle AE=\frac{1}{4} AC$ and $\displaystyle \overline{BE} \cap \overline{CF}=0$ prove $\displaystyle AO$ hits $\displaystyle \overline{BC}$ at its midpoint.