Editing Circle (section)

==Compass and straightedge constructions==
There are many [[compass-and-straightedge construction]]s resulting in circles.

The simplest and most basic is the construction given the centre of the circle and a point on the circle. Place the fixed leg of the [[Compass (drawing tool)|compass]] on the centre point, the movable leg on the point on the circle and rotate the compass.

===Construction with given diameter===
* Construct the [[midpoint]] {{math|'''M'''}} of the diameter.
* Construct the circle with centre {{math|'''M'''}} passing through one of the endpoints of the diameter (it will also pass through the other endpoint).

[[File:Circunferencia 10.svg|thumb|Construct a circle through points A, B and C by finding the perpendicular bisectors (red) of the sides of the triangle (blue). Only two of the three bisectors are needed to find the centre.]]

===Construction through three noncollinear points===
* Name the points {{math|'''P'''}}, {{math|'''Q'''}} and {{math|'''R'''}},
* Construct the [[perpendicular bisector]] of the segment {{math|{{overline|'''PQ'''}}}}.
* Construct the [[perpendicular bisector]] of the segment {{math|{{overline|'''PR'''}}}}.
* Label the point of intersection of these two perpendicular bisectors {{math|'''M'''}}. (They meet because the points are not [[collinear]]).
* Construct the circle with centre {{math|'''M'''}} passing through one of the points {{math|'''P'''}}, {{math|'''Q'''}} or {{math|'''R'''}} (it will also pass through the other two points).