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tetrahedron

Source: 6-th Taiwanese Mathematical Olympiad 1997

January 18, 2007
geometry3D geometrytetrahedrontrigonometryparallelogramgeometry proposed

Problem Statement

Let ABCDABCD is a tetrahedron. Show that a)If AB=CD,AC=DB,AD=BCAB=CD,AC=DB,AD=BC then triangles ABC,ABD,ACD,BCDABC,ABD,ACD,BCD are acute. b)If the triangles ABC,ABD,ACD,BCDABC,ABD,ACD,BCD have the same area , then AB=CD,AC=DB,AD=BCAB=CD,AC=DB,AD=BC.
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