$\textsf{\LARGE A}$

$\textsf{\LARGE B}$

Point - Point

When contracting the circles with the trace activated, at each point of the plane the color
corresponding to the closest center survives, so we obtain the perpendicular bisector.

Circumcenter

In the case of three points, we can visualize the circumcenter of the triangle that they determine.

XA - XB = 0

A = (0, 0)
B = (3.5, 0)
op1 = false
r = 0 (slider from 0 to 6, step 0.02)
A3: (0.75, 6)
A4: (4.5, 3.5)
A5: (-4.25, 2.5)
op2 = false
D = TriangleCenter(A3, A4, A5, 3)
n = Segment(A5, A3)
q = Segment(A3, A4)
s = Segment(A5, A4)
c = Circle(D, A5)
ci:=XA - XB = 0
r': 6 - r
d = Circle(B, r')
t = Circle(A, r')
B3 = Circle(A3, r')
B4 = Circle(A4, r')
B5 = Circle(A5, r')