2

Part of 1988 Romania Team Selection Test

Problems(1)

Another solid inequality with a trihedral angle

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

OABC

be a trihedral angle such that \angle BOC = \alpha, \angle COA = \beta, \angle AOB = \gamma , \alpha + \beta + \gamma = \pi . For any interior point

OP \geq PP_1+PP_2+PP_3

of the trihedral angle let

P_1

P_2

P_3

be the projections of

P

on the three faces. Prove that

OP \geq PP_1+PP_2+PP_3

. Constantin Cocea

inequalitiesgeometry proposedgeometry