Construcción de triángulo
Author: Angel Montesdeoca
Date: 11 Junio 2015

A'=M_a

A''=N_a

Locus of the symmedian K_1 of AB_1B'_1

''The symmedian point is the centroid of its pedal triangle''

A = (20.724037545231287, 37.5366194608417)
A' = (9.599698310017587, -2.292284002075755)
A'' = (22.228804663350363, -2.4081076746830754)
polígono1, m_a, a, b = Polygon(A, A', A'')
d = Line(A', A'')
B_1 = Point(d)
B'_1 = Mirror(B_1, A')
polígono2, b', a_1, b_1 = Polygon(A, B_1, B'_1)
K_1 = TriangleCenter(A, B_1, B'_1, 6)
A''' = Mirror(A'', A')
K' = TriangleCenter(A, A'', A''', 6)
e = Line(A', K')
f = Line(A, A'')
K = Intersect(e, f)
polígono3, D_1, E_1, F_1 = TrianguloPedal(A, B_1, B'_1, K_1)
g = OrthogonalLine(K, d)
D = Intersect(d, g)
M = puntoRazon(K, D, -1, 3)
polígono4, D', E', F' = TrianguloPedal(A, A''', A'', K')
h = Line(F', E')
i = Line(M, h)
j = Line(A', h)
k, K_2 = ConicaCuatroPuntosTangente(j, A', F', E', A)
F, E = Intersect(k, i)
l = Line(A, E)
m = Line(A, F)
B = Intersect(d, m)
C = Intersect(l, d)
polígono5, c_1, a_2, b_2 = Polygon(A, B, C)
polígono6, l_1, d_1, e_1 = Polygon(D, E, F)
n = Segment(A, A''')
h_a = Distance(A, d)
p = AngularBisector(A', A, A'')
V_a = Intersect(d, p)
v_a = Distance(A, V_a)
c = OrthogonalLine(A, d)
H_a = Intersect(d, c)
q = Segment(A', H_a)
G = Intersect(q, p)
o = Defined(G)
texto3: "V_a is on the segment  H_aM_a: " + o + ""

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: puntoRazon
Punto X que divide al segmento de extremos P y Q, según una razón  dada, PX : XQ = m : n
Input: P, Q, m, n
Output: X

X = Dilate(Q, m / (m + n), P)

Tool: Triangulo Pedal (command TrianguloPedal)
Dar ABC y P
Input: A, B, C, E
Output: polígono2, F, G, H

polígono1, c, a, b = Polygon(A, B, C)
e = OrthogonalLine(E, a)
f = OrthogonalLine(E, b)
g = OrthogonalLine(E, c)
h = Line(B, C)
i = Line(C, A)
j = Line(A, B)
F = Intersect(e, h)
G = Intersect(i, f)
H = Intersect(j, g)
polígono2, h_1, f_1, g_1 = Polygon(F, G, H)

Tool: Conica Cuatro Puntos Tangente (command ConicaCuatroPuntosTangente)
Dar una tangete, el punto de tangencia y tres puntos más
Input: t_P, P, P_1, P_3, P_2
Output: h, X

δ

Recta de Pascal

P = Point(t_P)
a = Line(P_2, P_3)
L = Intersect(a, t_P)
b = Line(L, P_1)
c = Line(P, P_2)
d = Line(P_3, P_1)
M = Intersect(c, d)
e = Line(M, L)
f = Line(P, P_3)
N = Intersect(e, f)
g = Line(P_2, N)
X = Intersect(b, g)
h = Conic(X, P_2, P, P_3, P_1)