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. This line segment crosses 
at
the midpoint 
of 
(middle figure). If the midpoint 
is known, then the perpendicular bisector can be constructed by drawing a small
auxiliary circle around 
,
then drawing an arc from each endpoint that crosses the line 
at the farthest intersection of the circle with the line (i.e., arcs with radii
and 
respectively). Connecting the intersections of the arcs then gives the
perpendicular bisector 
(right figure). Note that if the classical construction requirement that
compasses be collapsible is dropped, then the auxiliary circle can be omitted
and the rigid compass can be used to immediately draw the two arcs using any
radius larger that half the length of 
.
The perpendicular bisectors of a triangle
are lines passing through the midpoint 
of each side which are perpendicular to the
given side. A triangle's three perpendicular
bisectors meet (Casey 1888, p. 9) at a point 
known as the circumcenter (Durell
1928), which is also the center of the triangle's
circumcircle. 
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