Properties Of Triangles

Let $p_1, p_2$ and $p_3$ be the altitudes of a $\triangle A B C$ drawn through the vertices $A, B$ and $C$ respectively. If $r_1=4$, $r_2=6, r_3=12$ are the ex-radii of $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$