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Equilateral triangle picking..

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December 3, 2005
AMCAIMEgeometrycombinatorics

Problem Statement

Given the nine-sided regular polygon A1A2A3A4A5A6A7A8A9 A_1 A_2 A_3 A_4 A_5 A_6 A_7 A_8 A_9, how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set {A1,A2,...A9} \{A_1,A_2,...A_9\}? <spanclass=′latex−bold′>(A)</span> 30<spanclass=′latex−bold′>(B)</span> 36<spanclass=′latex−bold′>(C)</span> 63<spanclass=′latex−bold′>(D)</span> 66<spanclass=′latex−bold′>(E)</span> 72 <span class='latex-bold'>(A)</span> \ 30 \qquad <span class='latex-bold'>(B)</span> \ 36 \qquad <span class='latex-bold'>(C)</span> \ 63 \qquad <span class='latex-bold'>(D)</span> \ 66 \qquad <span class='latex-bold'>(E)</span> \ 72
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