2019 AMC 12B 第 11 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。
11.
给定一个立方体，有多少对无序的棱可以确定一个平面？
How many unordered pairs of edges of a given cube determine a plane?
小提示：
两条棱能确定一个平面，除非它们是异面直线
Two edges determine a plane unless they are skew
大提示：
分别数平行的棱对和共顶点的棱对
Count the pairs that are parallel and the pairs that share a vertex
解答：
两条棱恰好在共面时能确定一个平面，也就是它们平行或相交。
条棱分成 个方向，每个方向有 条平行棱，得到 对平行棱。共顶点的棱对有 对。
总数为 。
所以正确答案是 D。
Two edges determine a plane exactly when they are coplanar, that is, parallel or intersecting.
The edges split into directions of parallel edges, giving parallel pairs. Edges sharing a vertex give intersecting pairs.
The total is
Thus, D is the correct answer.
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