MathDB
2013 AMC 10A #25 on steroids

Source: 12B #19

November 17, 2021
AMCAMC 10AMC 10 BAMC 12AMC 12 B

Problem Statement

Regular polygons with 5,6,7,5, 6, 7, and 88 sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect?
<spanclass=latexbold>(A)</span> 52<spanclass=latexbold>(B)</span> 56<spanclass=latexbold>(C)</span> 60<spanclass=latexbold>(D)</span> 64<spanclass=latexbold>(E)</span> 68<span class='latex-bold'>(A)</span>\ 52 \qquad<span class='latex-bold'>(B)</span>\ 56 \qquad<span class='latex-bold'>(C)</span>\ 60 \qquad<span class='latex-bold'>(D)</span>\ 64 \qquad<span class='latex-bold'>(E)</span>\ 68