MathDB

6

Part of 1988 Austrian-Polish Competition

Problems(1)

pairwise orthogonal rays in space with a common start

Source: Austrian-Polish 1988

5/25/2019
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.
geometryangles3D geometryorthogonalrayacute triangleacute