BG-MO 1962 Problem 4

There are given a triangle and some internal point $P$ . $x,y,z$ are distances from $P$ to the vertices $A,B$ and $C$ . $p,q,r$ are distances from $P$ to the sides $BC,CA,AB$ respectively. Prove that: $$xyz\ge(q+r)(r+p)(p+q).$$