1996 AMC 8 第 25 题
先试着解答 1996 AMC 8 第 25 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 1996 AMC 8 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。
25.
在一个圆形区域内随机选取一点。该点到圆心的距离小于它到圆边界的距离的概率是多少？
A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region?
小提示：
一个点到圆心比到边界更近，当且仅当它到圆心的距离小于半径的一半。
A point is closer to the center than the boundary exactly when its distance from the center is less than half the radius
大提示：
比较半径为 的内圆面积与半径为 的整个圆面积。
Compare the area of the inner circle of radius to the whole circle of radius
解答：
设圆半径为 。距圆心 的点到圆心比到边界更近，当且仅当 ，即 。
有利区域是半径为 的圆，面积为 ，整个圆面积为 。概率为 。
所以正确答案是 A。
Take the radius to be A point at distance from the center is closer to the center than to the boundary when i.e.
The favorable region is a circle of radius with area out of the total area The probability is
Thus, the correct answer is A .
其他年份的第 25 题
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