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Another solid inequality with a trihedral angle

Source: Romanian IMO Team Selection Test TST 1988, problem 2

October 1, 2005
inequalitiesgeometry proposedgeometry

Problem Statement

Let OABCOABC be a trihedral angle such that \angle BOC = \alpha,   \angle COA = \beta,   \angle AOB = \gamma ,   \alpha + \beta + \gamma = \pi . For any interior point PP of the trihedral angle let P1P_1, P2P_2 and P3P_3 be the projections of PP on the three faces. Prove that OP≥PP1+PP2+PP3OP \geq PP_1+PP_2+PP_3. Constantin Cocea
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