Editing Bisection (section)

=== Construction by straight edge and compass ===
[[File:Mittelsenkr-ab-konstr-e.svg|thumb|upright=0.8|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 [[arc (geometry)|arc]]s of equal radii and different centers:

The segment <math>AB</math> is bisected by drawing intersecting circles of equal radius <math>r>\tfrac 1 2 |AB|</math>, 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.<br> 
Because the construction of the bisector is done without the knowledge of the segment's midpoint <math>M</math>, the construction is used for determining <math>M</math> 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'' <math>g</math> at a ''given point'' <math>P</math>: drawing a circle whose center is <math>P</math> such that it intersects the line <math>g</math> in two points <math>A,B</math>, and the perpendicular to be constructed is the one bisecting segment <math>AB</math>.