2020 AMC 8 第 18 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。
18.
矩形 内接于以 为直径的半圆，如图所示。已知 ，且 。矩形 的面积是多少？
Rectangle is inscribed in a semicircle with diameter as shown in the figure. Let and let What is the area of
小提示：
直径为
The diameter is
大提示：
用半径和矩形底边一半构造直角三角形
Use the radius and half the rectangle base in a right triangle
视频讲解：
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文字解答：
因为 是半圆直径，直径长为 ，半径为 。设 为直径的中点。
因此 的长度为 。
由于 在 上，
又因为该点在半圆上，所以 。
矩形 中， 是直角。用勾股定理求 ：
因此矩形面积为 。
正确答案是 A。
Since is the diameter of the semicircle, we know the length of the diameter is and so the radius is Let be the center of the diameter.
The length from therefore is
Since is on we know
Also, since we have a semicircle, we know
Finally, since is a rectangle, we know is a right angle. This means we can find by the Pythagorean Theorem. We know
Thus, the area of the rectangle is
Thus, the correct answer is A.
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