1997 AMC 8 第 24 题
先试着解答 1997 AMC 8 第 24 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 1997 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。
24.
点 将直径 按 分成两段。两个半圆 和 把圆形区域分成上方阴影区域和下方区域。上方区域面积与下方区域面积的比是
Diameter is divided at in the ratio The two semicircles, and divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region is
小提示：
把上方区域看成大半圆减去一个小半圆再加上另一个小半圆
Compare the upper region as a large semicircle minus one small semicircle plus the other
大提示：
选取符合 比例的方便长度
Choose convenient lengths in the ratio
解答：
取 ，使 、。大半圆半径为 ，面积为 。
以 为直径的半圆半径为 ，面积为 ；以 为直径的半圆半径为 ，面积为 。
上方阴影区域面积为
整个圆面积为 ，所以下方区域面积为 。
所求比为 。
所以正确答案是 C。
Choose so that and The large semicircle has radius so its area is
The semicircle on has radius and area while the semicircle on has radius and area
The upper shaded region has area
The whole circle has area so the lower region has area
The desired ratio is
Thus, C is the correct answer.
其他年份的第 24 题
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