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Two sets of diagonals in 7 gon are equal

Source: ToT 2003-JO-2

June 19, 2011
geometry unsolvedgeometry

Problem Statement

In 77-gon A1A2A3A4A5A6A7A_1A_2A_3A_4A_5A_6A_7 diagonals A1A3,A2A4,A3A5,A4A6,A5A7,A6A1A_1A_3, A_2A_4, A_3A_5, A_4A_6, A_5A_7, A_6A_1 and A7A2A_7A_2 are congruent to each other and diagonals A1A4,A2A5,A3A6,A4A7,A5A1,A6A2A_1A_4, A_2A_5, A_3A_6, A_4A_7, A_5A_1, A_6A_2 and A7A3A_7A_3 are also congruent to each other. Is the polygon necessarily regular?
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