KöMaL 2007 B3998

The vertex $P$ of a rectangular block with edges $a$, $b$, $c$ is selected. Consider the plane passing through the vertices adjacent to $P$. Denote the distance of the plane from $P$is $m$. Prove that $\frac{1}{m^2} = \frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}.$