1999 AMC 12 第 26 题
先试着解答 1999 AMC 12 第 26 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1999 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
26.
三个不重叠的正多边形，至少两个全等，边长都为 。这些多边形在点 处相接，使得在 处的三个内角之和为 。于是这三个多边形形成一个新的多边形，且 为内部点。这个新多边形的最大可能周长是多少？
Three non-overlapping regular plane polygons, at least two of which are congruent, all have sides of length The polygons meet at a point in such a way that the sum of the three interior angles at is Thus the three polygons form a new polygon with as an interior point. What is the largest possible perimeter that this polygon can have?
小提示：
若有两个 边形和一个 边形，则 。
With two -gons and one -gon,
大提示：
化简为 。
This simplifies to
解答：
设两个全等的多边形为正 边形，另一个为正 边形，在点 处相接。内角条件为 化简得 。
解为 等于 或 。新多边形的周长为 ，分别等于 和 。最大值为 。
所以正确答案是 D。
Let two congruent -gons and one -gon meet at Their interior angles satisfy which reduces to
The solutions are and The new polygon’s perimeter is giving and The largest is
Thus, the correct answer is D.
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