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P08 [Combinatorics] - Turkish NMO 1st Round - 2013

Source:

April 20, 2013

Problem Statement

How many kites are there such that all of its four vertices are vertices of a given regular icosagon (2020-gon)?
<spanclass=latexbold>(A)</span> 105<spanclass=latexbold>(B)</span> 100<spanclass=latexbold>(C)</span> 95<spanclass=latexbold>(D)</span> 90<spanclass=latexbold>(E)</span> 85 <span class='latex-bold'>(A)</span>\ 105 \qquad<span class='latex-bold'>(B)</span>\ 100 \qquad<span class='latex-bold'>(C)</span>\ 95 \qquad<span class='latex-bold'>(D)</span>\ 90 \qquad<span class='latex-bold'>(E)</span>\ 85