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GRE数学考试真题及解析(2)

  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?

  A. It contains no points.

  B. It contains one point.

  C. It contains two points.

  D. It is a line.

  E. It is a circle.

  解析

  答案:B

  解析:两条相连线段的中线只有一个焦点,到P和Q两点相同的点必定PQ的垂直平分线上, 到P和R两点相同的点也必定在PR的垂直平分线上,由于R不在PQ上,说明PQ的垂直平分线和PR的垂直平分线不平行,相交于一点,这一点到这PQR三点的距离相等,其实就是确定了一个圆心,不在一条直线上的三点确定一个圆。

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