The Circumcircle of a Triangle

Is a circle which passes through all three vertices of a triangle. See Math Open Reference. See also this simpler propane sketch, note the simplified collinearity test in the Points class, where we make use of Vec2D math (don’t try this with processings PVector class because, it doesn’t know whether it is 2D or 3D vector and hence deeply flawed).

Using Matrix Math

For detailed workings see Circumcircle at Mathworld Wolfram.com

a = { {x1 y1 1}, {x2 y2 1}, {x3 y3 1} }

bx = -{ {x12 + y12 y1 1}, {x22 + y22 y2 1}, {x32 + y32 y3 1} }

by = { {x12 + y12 x1 1}, {x22 + y22 x2 1}, {x32 + y32 x3 1} }

xo = -bx / 2 * a

yo = -by / 2 * a