Work out triangle circumcenter instantly with clear inputs, formula shown and shareable results.
The circumcentre is equidistant from all three vertices and is found where the perpendicular bisectors of the sides meet. Solving the two bisector equations gives the closed form used here.
Circumcentre
D = 2[xA(yB−yC) + xB(yC−yA) + xC(yA−yB)]; Ux, Uy from the squared-length sums divided by D
Yes. For an obtuse triangle it falls outside, and for a right triangle it sits exactly on the midpoint of the hypotenuse.
It means the points are collinear, so no unique circle passes through all three.