Prove using vectors line joining one of the vertices of a parallelogram to the midpoint of the opposite side intersects the diagonal in a ratio $1:2$.

Question

Label the four vertices of a parallelogram in counterclockwise order as OPQR. Prove that the line segment from $O$ to the midpoint of $PQ$ intersects the diagonal $PR$ in a point $X$ that is $1/3$ of the way from $P$ to $R$. I assumed $X$ is placed such that $\overrightarrow {PX}= a\ \overrightarrow {PR}$ and $\overrightarrow {XR}= b\ \overrightarrow {PR}$ but all I get after a bunch $f$ simplification is $a+b=1$ how do I proceed with this?