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  3. P, Q and R are three points in a plane, and R does not lie on line PQ. Which of

P, Q and R are three points in a plane, and R does not lie on line PQ. Which of

游客2025-02-23  23
问题 P, Q and R are three points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all points in the plane that are the same distance from all three points?
选项 A、It contains no point.
B、It contains one point.
C、It contains two points.
D、It is a line.
E、It is a circle.
答案 B
解析 不共线的三个点可以组成三角形，到这三个点距离都相等的点，只有一个，是三角形外接圆的圆心(外心)。外心是三角形三条边的中垂线的交点。外心到三个点的距离均为外接圆半径，符合题意。由于外心只有一个，故答案为B。
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