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A

**perpendicular bisector of a line segment**is a

**line segment perpendicular**to and passing through the midpoint of (left figure). The

**perpendicular bisector of a line segment**can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

Regards!

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A line segment bisector passes through the midpoint of the segment. Particularly important is the perpendicular bisector of a segment, which, according to its name, meets the segment at right angles. The perpendicular bisector of a segment also has the property that each of its points is equidistant from the segment's endpoints. Therefore, Voronoi diagram boundaries consist of segments of such lines or planes.

In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw circles of equal radii and different centers. The segment is bisected by drawing intersecting circles of equal radius, whose centers are the endpoints of the segment and such that each circle goes through one endpoint. 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. This construction is in fact used when constructing a line perpendicular to a given line at a given point: drawing an arbitrary circle whose center is that point, it intersects the line in two more points, and the perpendicular to be constructed is the one bisecting the segment defined by these two points.

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A

**perpendicular bisector of a line segment**is a

**line segment perpendicular**to and passing through the midpoint of (left figure). The

**perpendicular bisector of a line segment**can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

Regards!

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