<p>Convex polygons <img alt="$P_1$" height="17" src="https://latex.artofproblemsolving.com/a/5/b/a5b0256a78d58b6d5f7a53400b19e7747d2983fa.png" width="21" /> and <img alt="$P_2$" height="17" src="https://latex.artofproblemsolving.com/1/0/7/107c7c8e5a64d81ed24331e510b777b7d08345b7.png" width="21" /> are drawn in the same plane with <img alt="$n_1$" height="10" src="https://latex.artofproblemsolving.com/d/e/f/defbf06b987965438e5928b96688e48df84cba0e.png" width="16" /> and <img alt="$n_2$" height="10" src="https://latex.artofproblemsolving.com/8/5/c/85c5df946080fc6ec1ee0a560a8e8c5e6699113c.png" width="17" /> sides, respectively, <img alt="$n_1\le n_2$" height="14" src="https://latex.artofproblemsolving.com/e/9/1/e917d0fa3ed636b8e95c4b4b2ae9d1a7a1d429b3.png" width="59" />. If <img alt="$P_1$" height="17" src="https://latex.artofproblemsolving.com/a/5/b/a5b0256a78d58b6d5f7a53400b19e7747d2983fa.png" width="21" /> and <img alt="$P_2$" height="17" src="https://latex.artofproblemsolving.com/1/0/7/107c7c8e5a64d81ed24331e510b777b7d08345b7.png" width="21" /> do not have any line segment in common, then the maximum number of intersections of <img alt="$P_1$" height="17" src="https://latex.artofproblemsolving.com/a/5/b/a5b0256a78d58b6d5f7a53400b19e7747d2983fa.png" width="21" /> and <img alt="$P_2$" height="17" src="https://latex.artofproblemsolving.com/1/0/7/107c7c8e5a64d81ed24331e510b777b7d08345b7.png" width="21" /> is:</p> <p> </p>

Question No: 487

Convex polygons $P_1$ and $P_2$ are drawn in the same plane with $n_1$ and $n_2$ sides, respectively, $n_1\le n_2$ . If $P_1$ and $P_2$ do not have any line segment in common, then the maximum number of intersections of $P_1$ and $P_2$ is:

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Tags: Geometry

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