X(3)    CIRCUMCENTER

The circumcenter, labeled 3, is the point 
of concurrence of the perpendicular 
bisectors of the sides.  X(3) is the center 
of the circumcircle.

Sketch contributed by Michael Stairs,
January 2018.

Drag A, B, C.

3

A = (2.3000615632961208, 4.31177283166244)
B = (-0.2573193160656448, 1.9093847328680538)
C = (3.641627457866125, 1.8472026016204806)
f = Segment(B, A)
g = Segment(A, C)
h = Segment(C, B)
i = AngularBisector(B, C, A)
j = AngularBisector(C, B, A)
C' = Midpoint(f)
B' = Midpoint(g)
A' = Midpoint(h)
k = OrthogonalLine(C', f)
l = OrthogonalLine(B', g)
m = OrthogonalLine(A', h)
D = Point(m)
n = Ray(A', D)
E = Intersect(k, l)
c = Circle(E, C)
F = Intersect(h, n)
G = Intersect(l, g)
H = Intersect(k, f)