2024 AMC 8 第 6 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。
6.
Sergei 沿不同路线绕冰场滑行。下图中标出的线显示了四条路线，分别标为 P、Q、R、S。按从短到长排列，这四条路线的顺序是什么？
Sergei skated around an ice rink, gliding along different paths. The marked lines in the figures below show four of the paths labeled P, Q, R, and S. What is the sorted order of the four paths from shortest to longest?
P, Q, R, S
P, R, S, Q
Q, S, P, R
R, P, S, Q
R, S, P, Q
答案：D
视频讲解：
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文字解答：
R 最短，因为它用直线弦替代了较长的弧线部分。
Q 最长，因为它既包含弯曲端部，又有最多的内部交叉距离。
比较 P 和 S 时，S 中对应的直线段是一个对角线，而 P 中对应的是同一直角三角形的一条边。
对角线更长，所以 S 比 P 长。从短到长为 R、P、S、Q。正确答案是 D。
Path R is shortest because it replaces curved arc portions with straight-line chords. Path Q is longest because it includes the most interior crossing distance while still using the curved ends.
It remains to compare paths P and S. The relevant straight piece in path S is a diagonal across the rink, while the corresponding straight piece in path P is a side of the same right triangle. A diagonal is longer than a side, so path S is longer than path P.
The order from shortest to longest is R, P, S, Q.
Thus, D is the correct answer.
其他年份的第 6 题
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