2010 AMC 8 第 19 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。
19.
图中的两个圆有相同的圆心 。弦 在 点与内圆相切， 长 ，且弦 长 。两个圆之间区域的面积是多少？
The two circles pictured have the same center Chord is tangent to the inner circle at is and chord has length What is the area between the two circles?
小提示：
半条弦、内圆半径和外圆半径组成一个直角三角形
Half the chord, the inner radius, and the outer radius form a right triangle.
大提示：
指向切点的半径垂直于切线
The radius to a tangent point is perpendicular to the chord.
解答：
两圆之间的面积等于大圆面积减去小圆面积，即 由勾股定理，因此只需求 。
因为 是 的一半，所以 。于是 。
所以正确答案是 C。
The area between the two circles is the area of the larger circle minus the area of the smaller circle. This would be By the Pythagorean Theorem, we can get Therefore, we need to find
Since is half of we get This makes
Thus, the answer is C .
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