quality:correction, stylistic:tone, information:filtering, information:extraction
Construction by straight edge and compass

In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw arcs of equal radii and different centers:

The segment A B {\displaystyle AB} is bisected by drawing intersecting circles of equal radius r > 1 2 | A B | {\displaystyle r>{\tfrac {1}{2}}|AB|}, whose centers are the endpoints of the segment. The line determined by the points of intersection of the two circles is the perpendicular bisector of the segment. Because the construction of the bisector is done without the knowledge of the segment's midpoint M {\displaystyle M}, the construction is used for determining M {\displaystyle M} as the intersection of the bisector and the line segment.

This construction is in fact used when constructing a line perpendicular to a given line g {\displaystyle g} at a given point P {\displaystyle P}: drawing a circle whose center is P {\displaystyle P} such that it intersects the line g {\displaystyle g} in two points A, B {\displaystyle A,B}, and the perpendicular to be constructed is the one bisecting segment A B {\displaystyle AB}.