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1968 AMC 12 #30 - Intersections of Polygons

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January 1, 2012
AMC

Problem Statement

Convex polygons P1P_1 and P2P_2 are drawn in the same plane with n1n_1 and n2n_2 sides, respectively, n1≤n2n_1 \le n_2. If P1P_1 and P2P_2 do not have any line segment in common, then the maximum number of intersections of P1P_1 and P2P_2 is:
<spanclass=′latex−bold′>(A)</span> 2n1<spanclass=′latex−bold′>(B)</span> 2n2<spanclass=′latex−bold′>(C)</span> n1n2<spanclass=′latex−bold′>(D)</span> n1+n2<spanclass=′latex−bold′>(E)</span> none of these<span class='latex-bold'>(A)</span>\ 2n_1 \qquad<span class='latex-bold'>(B)</span>\ 2n_2 \qquad<span class='latex-bold'>(C)</span>\ n_1n_2 \qquad<span class='latex-bold'>(D)</span>\ n_1+n_2 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these}
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