1968 AMC 12 第 30 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
30.
在同一平面内画有凸多边形 和 ，其边数分别为 和 ，且 。若 与 没有任何公共线段，则 与 交点数的最大值为：
Convex polygons and are drawn in the same plane with and sides, respectively, If and do not have any line segment in common, then the maximum number of intersections of and is:
以上皆非
none of these
小提示：
一条线段至多只能进入并离开一个凸多边形一次
A line segment can enter and leave a convex polygon at most once
大提示：
对边数较少的多边形的每一条边应用这一上界
Apply that bound to each side of the polygon with fewer sides
解答：
的每条边都位于一条直线上，它与凸区域 的交集要么是一条线段，要么为空。因此该边与 的边界至多相交两次。对 条边合计，交点数至多为 ；取适当的狭长凸 边形穿过一个凸 边形即可达到此上界。
因此，正确答案是 A。
Each side of lies on a line, and its intersection with the convex region is a single segment or empty. Thus that side crosses the boundary of at most twice. Across sides there are at most and a suitable thin convex -gon crossing a convex -gon attains this bound.
Therefore, the correct answer is A.
其他年份的第 30 题
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- 1973 AMC 12
- 1974 AMC 12
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- 1978 AMC 12
- 1979 AMC 12
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- 1981 AMC 12
- 1982 AMC 12
- 1983 AMC 12
- 1984 AMC 12
- 1985 AMC 12
- 1986 AMC 12
- 1987 AMC 12
- 1988 AMC 12
- 1989 AMC 12
- 1990 AMC 12
- 1991 AMC 12
- 1992 AMC 12
- 1993 AMC 12
- 1994 AMC 12
- 1995 AMC 12
- 1996 AMC 12
- 1997 AMC 12
- 1998 AMC 12
- 1999 AMC 12