P*

P*

 I' - >0.812149174855214 

A'B'C' triángulo ceviano de X_1
O'  circuncentro de A'B'C'
P  conj. isogonal de X_1 resp, a A'B'C'
P' inverso de P en la circunf. circunscrita a A'B'C'
Q conjugado antigonal de X_1 resp. a A'B'C'

(A_a)

(B_b)

(C_c)

A = (4.02905716994755, 0.6597953206464334)
B = (19.753724337992214, 1.0862831568091242)
C = (13.826397676819585, 7.1705521849440474)
polígono1, c, a, b = Polygon(A, B, C)
X_1 = TriangleCenter(A, B, C, 1)
polígono2, A', B', C' = TrianguloCeviano(A, B, C, X_1)
d = Circle(C', A', B')
P = ConjugadoIsogonal(A', B', C', X_1)
e = Polar(P, d)
O' = Center(d)
f = Line(O', P)
P' = Intersect(e, f)
Q = ConjugadoIsogonal(A', B', C', P')
g = Line(X_1, O')
h = Segment(A, A')
i = Segment(B, B')
j = Segment(C, C')
X_{399} = TriangleCenter(A, B, C, 399)
B'_a = Mirror(B', h)
C'_a = Mirror(C', h)
k = OrthogonalLine(B'_a, i)
l = OrthogonalLine(C'_a, j)
A'_a = Intersect(k, l)
Aa = Circle(A'_a, C'_a, B'_a)
Bb = CicunferenciaAa(B, C, A)
Cc = CicunferenciaAa(C, A, B)
D = Center(Bb)
m = OrthogonalLine(D, a)
A'' = Mirror(A', m)
n = OrthogonalLine(D, c)
C'' = Mirror(C', n)
E = Center(Cc)
p = OrthogonalLine(E, a)
A''_1 = Mirror(A', p)
q = OrthogonalLine(E, b)
B'' = Mirror(B', q)

Tool: Triangulo Ceviano (command TrianguloCeviano)
Dar ABC y P
Input: A, B, C, P
Output: polígono2, A', B', C'

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(A, P)
h = Line(B, P)
i = Line(C, P)
A' = Intersect(d, g)
B' = Intersect(e, h)
C' = Intersect(f, i)
polígono2, f_1, d_1, e_1 = Polygon(A', B', C')

Tool: Conjugado Isogonal (command ConjugadoIsogonal)
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: G

P*

polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(P, b)
e = OrthogonalLine(P, a)
f = OrthogonalLine(P, c)
g = Line(A, B)
h = Line(B, C)
i = Line(C, A)
D = Intersect(g, f)
E = Intersect(d, i)
F = Intersect(h, e)
k = Line(E, F)
l = Line(F, D)
n = OrthogonalLine(B, l)
p = OrthogonalLine(C, k)
G = Intersect(n, p)

Tool: Conjugado Antigonal De I (command ConjugadoAntigonalDeI)
Dar ABC
Input: A, B, C
Output: I

P*

P*

X_1 = TriangleCenter(A, B, C, 1)
polígono2, D, E, F = TrianguloCeviano(A, B, C, X_1)
d = Circle(F, D, E)
G = ConjugadoIsogonal(D, E, F, X_1)
e = Polar(G, d)
O' = Center(d)
f = Line(O', G)
H = Intersect(e, f)
I = ConjugadoIsogonal(D, E, F, H)

Tool: Cicunferencia Aa (command CicunferenciaAa)
Dar ABC
Input: A, B, C
Output: p

X_1 = TriangleCenter(A, B, C, 1)
polígono2, A', B', C' = TrianguloCeviano(A, B, C, X_1)
h = Segment(A, A')
i = Segment(B, B')
j = Segment(C, C')
B'_a = Mirror(B', h)
C'_a = Mirror(C', h)
k = OrthogonalLine(B'_a, i)
l = OrthogonalLine(C'_a, j)
A'_a = Intersect(k, l)
p = Circle(A'_a, C'_a, B'_a)