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good triangles in a plane, triangle construction related

Source: Israel Grosman Memorial Mathematical Olympiad 2001 p5

February 15, 2020
constructiongeometric constructiongeometry

Problem Statement

Triangle ABCABC in the plane Π\Pi is called good if it has the following property: For any point DD in space outside the plane Π\Pi, it is possible to construct a triangle with sides of lengths CD,BD,ADCD,BD,AD. Find all good triangles
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