How can I prove this problem on geometry? I need to prove the following:

If $P$ is an inner point of $\triangle ABC$, then there is a single transverse $EF$ of $\overleftrightarrow{AB}$ and $\overleftrightarrow{AC}$, where $E$ is on $\overleftrightarrow{AC}$ and $F$ is on $\overleftrightarrow{AB}$, such that P is the middle of the segment $XY$.

I tried for a longer time but nothing!! Some idea? Thanks in advance.

Just a hint : You can always make a parallelogram out of A and P, where A is a vertex and P is the center of the parallelogram itself
