Let $\displaystyle AD$, $\displaystyle BE$, $\displaystyle CF$ be three cevians concurrent at $\displaystyle P$ inside the $\displaystyle \Delta ABC$.
Prove or disprove that:
$$\displaystyle \dfrac{AD}{AP} + \dfrac{BE}{BP} + \dfrac{CF}{CP} \ge \dfrac{9}{2}$$