Prove that $\frac{1}{q}+\frac{1}{p}>\frac{1}{r}$ when you know that:

Question

Let $ABC$ be a triangle. Two points $P$ and $Q$ are on sides $AB$ and $AC$, respectively. The point $R$ is the intersection of lines $BQ$ and $CP$. The distances from the points $P$, $Q$, and $R$ to the side $BC$ are $p$, $q$, and $r$, respectively. Prove that $$\frac{1}{p}+\frac{1}{q}>\frac{1}{r}.$$