NL-NWO 2006 Problem 2

Given is a acute angled triangle $ABC$ . The lengths of the altitudes from $A, B$ and $C$ are successively $h_A, h_B$ and $h_C$ . Inside the triangle is a point $P$ . The distance from $P$ to $BC$ is $1/3 h_A$ and the distance from $P$ to $AC$ is $1/4 h_B$ . Express the distance from $P$ to $AB$ in terms of $h_C$ .