In two-dimensional Euclidean geometry the locus of points equidistant from two given ( different ) points is their perpendicular bisector.
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A triangle with exactly two equal sides has exactly one axis of symmetry, which goes through the perpendicular bisector of the base.
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The perpendicular bisector of a side of a triangle is the line that is perpendicular to that side and passes through its midpoint.
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The perpendicular bisector of line segment SS'is the Lemoine line, which contains the three centers of the circles of Apollonius.
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The locus of points equidistant from two given points is a straight line that is called the perpendicular bisector of the line segment connecting the points.
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The center of the solution circle is equally distant from all three points, and therefore must lie on the perpendicular bisector line of any two.
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However, it does not include all points of the rectangle; for instance, the perpendicular bisector of the initial line segment is not included.
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:: : A fact that may be helpful is that the set of points equidistant from two given points, the perpendicular bisector, is flat.
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The line determined by the points of intersection of the two circles is the perpendicular bisector of the segment, since it crosses the segment at its center.
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The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly bisects that side.
