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pairwise orthogonal rays in space with a common start

Source: Austrian-Polish 1988

May 25, 2019
geometryangles3D geometryorthogonalrayacute triangleacute

Problem Statement

Three rays h1,h2,h3h_1,h_2,h_3 emanating from a point OO are given, not all in the same plane. Show that if for any three points A1,A2,A3A_1,A_2,A_3 on h1,h2,h3h_1,h_2,h_3 respectively, distinct from OO, the triangle A1A2A3A_1A_2A_3 is acute-angled, then the rays h1,h2,h3h_1,h_2,h_3 are pairwise orthogonal.
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