Free · Mathematical relationships

Triangle Circumcenter from Coordinates

Three noncollinear vertices determine a unique circumcircle. A right triangle’s circumcenter is the midpoint of its hypotenuse.

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With x1 = 0, y1 = 0, x2 = 4, y2 = 0, x3 = 0, y3 = 6, res_x = 2, res_y = 3.

The center has equal squared distance to all three vertices.

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Three noncollinear vertices determine a unique circumcircle. A right triangle’s circumcenter is the midpoint of its hypotenuse.
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The center has equal squared distance to all three vertices.

The determinant of two vertex displacement vectors must be nonzero: collinear vertices do not determine a unique circumcircle.