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MMO 320 Moscow MO 1956 triangles ABC,BCD,CDA,DAB not all acute

Source:

August 19, 2019
acutegeometryangles

Problem Statement

Prove that there are no four points A,B,C,DA, B, C, D on a plane such that all triangles △ABC,△BCD,△CDA,△DAB\vartriangle ABC,\vartriangle BCD, \vartriangle CDA, \vartriangle DAB are acute ones.
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