AMC 8 2025 Problem 12
AMC8 2025 年第 12 题
圆★★★☆☆
The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?
下图所示区域由24个边长为1厘米的正方形组成。请问该区域内正好能够容纳的最大圆的面积是多少平方厘米？（最大圆可能会接触到边界）
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
The largest circle that can fit inside the figure has its center in the middle of the figure and will be tangent to the figure in 8 points. By the Pythagorean Theorem, the distance from the center to one of these 8 points is , so the area of this circle is 𝜋 5 2 = (C) 5 𝜋.
Draw the circle in the grid and analyze the radius. Its radius is a little more than 2 but a lot less than 2.5, so the area is a little more than 4π. So, the area of the circle is with a radius of approximately 2.23.
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