2. 外语
  3. In the xy-plane, the point with coordinates(-6,-7)is the center of circle C. The point with coordinates(-6, 5)lies inside C, and

In the xy-plane, the point with coordinates(-6,-7)is the center of circle C. The point with coordinates(-6, 5)lies inside C, and

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问题 In the xy-plane, the point with coordinates(-6,-7)is the center of circle C. The point with coordinates(-6, 5)lies inside C, and the point with coordinates(8, -7)lies outside C. If m is the radius of C and m is an integer, what is the value of m ?
m =______
选项
答案13
解析 A strategy that is often helpful in working with geometry problems is drawing a figure that represents the given information as accurately as possible.
    In this question you are given that the point with coordinates(-6,-7)is the center of circle C, the point with coordinates(—6, 5)lies inside circle C, and the point with coordinates(8, -7)lies outside circle C, so you could draw the following figure.

    From the figure, you can see that the distance between(-6,-7)and(-6, 5)is 7 + 5, or 12, and the radius of C must be greater than 12. You can also see that the distance between(-6, -7)and(8, -7)is 6 + 8, or 14, and the radius of C must be less than 14. Therefore, since the radius is an integer greater than 12 and less than 14, it must be 13. The correct answer is 13.
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