2026 AMC 8 第 23 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。
23.
Lakshmi 有 枚圆形硬币，每枚直径为 厘米。她把硬币按图中 行摆在桌上，并用一根弹性带紧紧围住它们。弹性带的长度是多少厘米？
Lakshmi has round coins of diameter centimeters. She arranges the coins in rows on a table top, as shown below, and wraps an elastic band tightly around them. In centimeters, what will be the length of the band?
小提示：
先沿硬币圆心的外轮廓看直线部分。
Trace the path followed by the centers of the coins
大提示：
弹性带长度等于圆心外轮廓的周长，再加上半径为 的一整圈圆周长。
Add the center-hull perimeter and one full circumference of radius
视频讲解：
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文字解答：
追踪这些硬币圆心的路径。圆心形成的凸包是一个梯形，底边为 ，上底为 ，两条斜边长度都是 ，所以周长为 。硬币半径为 ，弹性带绕过圆角时额外增加一个完整圆周，长度为 。因此弹性带长度为 。
Trace the path of the centers of the coins. Their convex hull is a trapezoid with bottom side , top side , and two slanted sides of length , so its perimeter is . Wrapping the band around coins of radius adds one full circumference, . The band length is .
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