Cercles de Miquel
Author: Patrice Debart

A = (1, -4)
B = (6, -2)
C = (5, 0)
D = (2, 1)
dAB = Line(A, B)
dCD = Line(D, C)
dAD = Line(A, D)
dBC = Line(B, C)
E = Intersect(dAB, dCD)
F = Intersect(dAD, dBC)
AE = Segment(A, E)
AF = Segment(A, F)
BF = Segment(B, F)
DE = Segment(D, E)
c_1 = Circle(A, D, E)
c_2 = Circle(B, C, E)
c_3 = Circle(A, B, F)
c_4 = Circle(C, D, F)
M = Intersect(c_3, c_4, 2.0)
O_1 = Centre_cercle(A, D, E)
O_2 = Centre_cercle(B, C, E)
O_3 = Centre_cercle(A, B, F)
O_4 = Centre_cercle(F, C, D)
c = Circle(O_1, O_2, O_3)

Tool: Centre cercle circonscrit (command Centre_cercle)
A partir de trois points du cercle
Input: A, B, C
Output: O

d1 = LineBisector(A, B)
d2 = LineBisector(B, C)
O = Intersect(d1, d2)