CMO 2015 Problem 2

Let $A B C$ be an acute-angled triangle with altitudes $A D, B E$, and $C F$. Let $H$ be the orthocentre, that is, the point where the altitudes meet. Prove that

$$\frac{A B \cdot A C+B C \cdot B A+C A \cdot C B}{A H \cdot A D+B H \cdot B E+C H \cdot C F} \leq 2 .$$