RO-TST 1988 Problem 2

Let $OABC$ be a trihedral angle such that $$\angle BOC = \alpha, \angle COA = \beta, \angle AOB = \gamma , \alpha + \beta + \gamma = \pi .$$ For any interior point $P$ of the trihedral angle let $P_1$ , $P_2$ and $P_3$ be the projections of $P$ on the three faces. Prove that $OP \geq PP_1+PP_2+PP_3$ .

Constantin Cocea