$\mbox{P}(u:v:w)$

trilinear polar of P

$Q^a$

$Q^b$

$Q^c$

U

V

W

 T(P,\textstyle{-\frac{5}{4}})

$ \left(\frac{x}{u}+\frac{y}{v}+\frac{z}{w}\right) 
\left(\frac{u}{x}+\frac{v}{y}+\frac{w}{z}\right)  = -\frac{5}{4}$

P = (12.902070410976918, -3.953240049322791)
C = (6.939259445487121, 2.856619182819244)
B = (9.311778784431823, -1.381835801064813)
A = (-1.3282212155681803, -1.221835801064813)
texto1, bP = CoordenadasBaricentrias(A, B, C, P)
w = Element(bP, 3)
v = Element(bP, 2)
u = Element(bP, 1)
i = TriangleCurve(A, B, C, 4 * B * C^(2) * u^(2) * v + 4 * A * C^(2) * u * v^(2) + 4 * B^(2) * C * u^(2) * w + 17 * A * B * C * u * v * w + 4 * A^(2) * C * v^(2) * w + 4 * A * B^(2) * u * w^(2) + 4 * A^(2) * B * v * w^(2) = 0)
polígono1, c, a, b = Polygon(A, B, C)
d = Tripolar(A, B, C, P)
Q = Point(i)
polígono2, Q_a, Q_b, Q_c = TrianguloCeviano(A, B, C, Q)
e = Line(C, B)
f = Line(C, A)
g = Line(A, B)
U = Intersect(d, e)
V = Intersect(f, d)
W = Intersect(d, g)
polígono3, G, H, I = TrianguloAnticeviano(A, B, C, Q)
j = Line(Q_a, V)
k = Line(Q_a, W)
l = Line(H, I)
A_b = Intersect(l, j)
A_c = Intersect(k, l)
m = Line(I, G)
n = Line(Q_b, U)
s = Line(Q_b, W)
B_a = Intersect(n, m)
B_c = Intersect(m, s)
t = Line(H, G)
a_1 = Line(Q_c, V)
C_b = Intersect(t, a_1)
b_1 = Line(Q_c, U)
C_a = Intersect(t, b_1)
c_1 = Conic(A_b, A_c, C_b, C_a, B_a)

Tool: TrianguloETC
Dar el vértice A
Input: A_{etc}
Output: B_{etc}, C_{etc}, a, polígono1

c = Circle(A_{etc}, 13)
B_{etc} = Point(c)
d = Circle(A_{etc}, 9)
e = Circle(B_{etc}, 6)
C_{etc} = Intersect(d, e, 1)
polígono1, c_{etc}, a_{etc}, b_{etc} = Polygon(A_{etc}, B_{etc}, C_{etc})
a = Line(B_{etc}, C_{etc})

Tool: Coordenadas Trilineales (command CoordenadasTrilineales)
Dar los vértices de ABC y un  punto P
Input: A, B, C, P
Output: texto2, CoordTrilineales

q_1 = Segment(B, P)
e = Line(A, C)
E_1 = Intersect(e, q_1)
d = Line(C, B)
p_1 = Segment(A, P)
D_1 = Intersect(d, p_1)
ABC, c, a, b = Polygon(A, B, C)
e_1 = OrthogonalLine(P, a)
D = Intersect(e_1, d)
p = Segment(P, D)
α = If(Defined[D_1], -p, p)
f_1 = OrthogonalLine(P, b)
g = OrthogonalLine(P, c)
f = Line(A, B)
E = Intersect(f_1, e)
F = Intersect(g, f)
r_1 = Segment(P, C)
q = Segment(P, E)
r = Segment(P, F)
F_1 = Intersect(f, r_1)
β = If(Defined[E_1], -q, q)
γ = If(Defined[F_1], -r, r)
CoordTrilineales: {α, β, γ}
texto2: "" + CoordTrilineales + ""

Tool: Coordenadas Baricentrias (command CoordenadasBaricentrias)
Dar los vértices ABC y un punto P
Input: A, B, C, P
Output: texto2, CoordBaricentricas

q_1 = Segment(B, P)
APB, b_2, a_2, p_4 = Polygon(A, P, B)
e = Line(A, C)
E_1 = Intersect(e, q_1)
CPA, a_1, c_2, p_3 = Polygon(C, P, A)
BPC, c_1, b_1, p_2 = Polygon(B, P, C)
d = Line(C, B)
p_1 = Segment(A, P)
D_1 = Intersect(d, p_1)
f = Line(A, B)
r_1 = Segment(P, C)
F_1 = Intersect(f, r_1)
xx = If(Defined[D_1], -BPC, BPC)
yy = If(Defined[E_1], -CPA, CPA)
zz = If(Defined[F_1], -APB, APB)
CoordBaricentricas: {xx, yy, zz}
texto2: "" + CoordBaricentricas + ""

Tool: Tripolar
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: l

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(P, A)
h = Line(P, B)
i = Line(P, C)
E = Intersect(h, e)
F = Intersect(d, g)
j = Line(E, F)
G = Intersect(f, i)
k = Line(G, F)
H = Intersect(e, k)
I = Intersect(j, f)
l = Line(H, I)

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: Triangulo Anticeviano (command TrianguloAnticeviano)
Dar ABC y P
Input: A, B, C, P
Output: polígono3, 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)
j = Line(B', C')
k = Line(C', A')
D = Intersect(h, k)
m = Line(A, D)
E = Intersect(m, d)
n = Line(C', E)
A'' = Intersect(g, n)
F = Intersect(g, j)
p = Line(B, F)
G = Intersect(p, e)
q = Line(C', G)
B'' = Intersect(h, q)
r = Line(C, D)
H = Intersect(r, f)
s = Line(A', H)
C'' = Intersect(i, s)
polígono3, c'', a'', b'' = Polygon(A'', B'', C'')