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Turkish NMO First Round - 2012 Problem - 13 {Geometry}

Source:

July 1, 2012
geometryAsymptotevector

Problem Statement

2020 points with no three collinear are given. How many obtuse triangles can be formed by these points?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 20<spanclass=′latex−bold′>(C)</span> 2(103)<spanclass=′latex−bold′>(D)</span> 3(103)<spanclass=′latex−bold′>(E)</span> (203) <span class='latex-bold'>(A)</span>\ 6 \qquad <span class='latex-bold'>(B)</span>\ 20 \qquad <span class='latex-bold'>(C)</span>\ 2{{10}\choose{3}} \qquad <span class='latex-bold'>(D)</span>\ 3{{10}\choose{3}} \qquad <span class='latex-bold'>(E)</span>\ {{20}\choose{3}}
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