๐ Circumcenter Calculator
Calculate the circumcenter (center of circumscribed circle) coordinates of a triangle.
Vertex A:
Vertex B:
Vertex C:
What is the Circumcenter?
The point where the three perpendicular bisectors of a triangle meet. All three vertices are equidistant from the circumcenter, and this distance is the circumscribed circle radius (R).
Circumcenter Coordinate Formula
D = 2[xโ(yโโyโ) + xโ(yโโyโ) + xโ(yโโyโ)]
Ox = [(xโยฒ+yโยฒ)(yโโyโ) + (xโยฒ+yโยฒ)(yโโyโ) + (xโยฒ+yโยฒ)(yโโyโ)] / D
Oy = [(xโยฒ+yโยฒ)(xโโxโ) + (xโยฒ+yโยฒ)(xโโxโ) + (xโยฒ+yโยฒ)(xโโxโ)] / D
Position of the Circumcenter
Acute triangle: inside the triangle
Right triangle: midpoint of the hypotenuse
Obtuse triangle: outside the triangle
Circumscribed Circle Radius
R = |OA| = |OB| = |OC|
R = abc / (4S)