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  3. In the figure above, x=2. What is the area of circle O?

In the figure above, x=2. What is the area of circle O?

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问题 In the figure above, x=2. What is the area of circle O?
选项 A、 
B、 
C、 
D、 
E、 
答案B
解析 Since we are looking for the area of the circle, we really need to find the radius. The line segment from the center of the circle to the vertex of the square is 2, so we can use that to find the radius. If you extend line x to the opposite vertex of the square, you have drawn a diagonal of that square, which is also the hypotenuse of a 45°-45°-90° triangle. The diagonal measures 4. You normally multiply a leg of a 45°-45°-90° triangle by to get the hypotenuse, so we have to divide the hypotenuse by to get the leg (which is also the side of the square and the diameter of the circle). Therefore, the diameter is equal to and the radius is equal to . But we’re not done; we still have to find the area. The formula for the area of a circle is A=nr2, so we have to substitute in for r. Squaring both the top and bottom of the fraction, we get 4/2 , or 2. So the area of the circle is 2π.
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