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Nine points, three pentagons, and one triangle in space

Source: XVIII Olimpíada Matemática Rioplatense (2009)

July 23, 2011
trigonometrygeometrycircumcircleparallelogramgeometry unsolved

Problem Statement

Let AA, BB, CC, DD, EE, FF, GG, HH, II be nine points in space such that ABCDEABCDE, ABFGHABFGH, and GFCDIGFCDI are each regular pentagons with side length 11. Determine the lengths of the sides of triangle EHIEHI.
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