Triangle Centres Demonstration

For fine movement of point P first select it and then use the Keyboard Arrow keys (Press and hold the SHIFT button at the same time as pressing the Arrow keys for even finer control)

Case 1

Construction 1

Case 2

Construction 2

Move point P so as to make all three circles coincide

A = (0.7273908476348725, 4.708494570593351)
B = (10.61613833581128, 1.2589314933225142)
C = (-3.4777908084667275, -5.081693972518173)
poly1, c, a, b = Polygon(A, B, C)
P = (4.242659888282297, 0.04337117085564659)
d = Circle(P, A)
e = Circle(P, C)
f = Circle(P, B)
E = Midpoint(c)
F = Midpoint(b)
G = Midpoint(a)
g = OrthogonalLine(E, c)
h = OrthogonalLine(F, b)
i = OrthogonalLine(G, a)
H = Intersect(i, g)
k = false
j = false
l = OrthogonalLine(P, b)
m = OrthogonalLine(P, c)
n = OrthogonalLine(P, a)
p = Line(A, C)
q = Line(C, B)
r = Line(B, A)
I = Intersect(l, p)
J = Intersect(n, q)
K = Intersect(m, r)
s = Circle(P, I)
t = Circle(P, J)
c_1 = Circle(P, K)
a_1 = Segment(B, K)
b_1 = Segment(B, J)
d_1 = Segment(C, I)
o = false
e_1 = AngularBisector(C, A, B)
f_1 = AngularBisector(B, C, A)
g_1 = AngularBisector(A, B, C)
h_1 = OrthogonalLine(B, g_1)
i_1 = OrthogonalLine(C, f_1)
j_1 = OrthogonalLine(A, e_1)
L = Intersect(j_1, h_1)
M = Intersect(h_1, i_1)
N = Intersect(i_1, j_1)
O = Intersect(f_1, e_1)
u = false