Editing Midpoint (section)

==Construction==
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a [[compass and straightedge construction]]. The midpoint of a line segment, embedded in a [[Plane (geometry)|plane]], can be located by first constructing a [[Lens (geometry)|lens]] using [[circular arc]]s of equal (and large enough) [[radius|radii]] centered at the two endpoints, then connecting the [[cusp (singularity)|cusp]]s of the lens (the two points where the arcs intersect). The point where the line connecting the cusps intersects the segment is then the midpoint of the segment. It is more challenging to locate the midpoint using only a compass, but it is still possible according to the [[Mohr-Mascheroni theorem]].<ref>{{cite web|url=http://mathworld.wolfram.com/Midpoint.html|title=Wolfram mathworld|date=29 September 2010}}</ref>