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IMC 2002 Problem 10

Source: IMC 2002 Day 2 Problem 4

October 27, 2020
3D geometrytetrahedroninequalities

Problem Statement

Let OABCOABC be a tetrahedon with ∠BOC=α,∠COA=β\angle BOC=\alpha,\angle COA =\beta and ∠AOB=γ\angle AOB =\gamma. The angle between the faces OABOAB and OACOAC is σ\sigma and the angle between the faces OABOAB and OBCOBC is ρ\rho. Show that γ>βcos⁡σ+αcos⁡ρ\gamma > \beta \cos\sigma + \alpha \cos\rho.
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