Médianes

Médiatrices

Hauteurs

Somme des angles

Bissectrices

Euler (Droite)

Euler (Cercle)

A = (13.879456811274329, 1.2750923709176647)
B = (16.21017786884086, -3.266825587417115)
C = (9.297697467340122, -4.063653299405672)
poly1, c, a, b = Polygon(A, B, C)
m2 = LineBisector(b)
m1 = LineBisector(a)
m3 = LineBisector(c)
O_c = Intersect(m2, m1)
mCirc = Circle(O_c, C)
h1 = OrthogonalLine(A, a)
h3 = OrthogonalLine(C, c)
h2 = OrthogonalLine(B, b)
Orthocentre = Intersect(h1, h3)
Biss_1 = AngularBisector(B, A, C)
Biss_2 = AngularBisector(C, B, A)
Biss_3 = AngularBisector(A, C, B)
O_i = Intersect(Biss_3, Biss_2)
ζ = Angle(c, h3)
δ = Angle(a, h1)
ε = Angle(b, h2)
α, β, γ = Angle(poly1)
Σ: α + β + γ
h = OrthogonalLine(O_i, c)
D = Intersect(c, h)
BissIns = Circle(O_i, D)
I_1 = Midpoint(C, B)
I_2 = Midpoint(A, B)
I_3 = Midpoint(A, C)
Méd_1 = Line(A, I_1)
Méd_3 = Line(C, I_2)
Méd_2 = Line(B, I_3)
Barycentre = Intersect(Méd_3, Méd_1)
DroiteEuler = Line(Orthocentre, O_c)
CercleEuler = Circle(I_2, I_1, I_3)
Sommedesangles: "Σ = α + β + γ = " + α + " + " + β + " + " + γ + " = " + Σ
η = Angle(c, m3)
θ = Angle(a, m1)
ι = Angle(b, m2)
distanceO_cBarycentre = Distance(O_c, Barycentre)
d = Distance(O_c, Barycentre)
distanceBarycentreOrthocentre = Distance(Barycentre, Orthocentre)
d_{BaryCirc}: "\overline{O_C Barycentre} \, = \," + d
d_{BaryOrtho}: "\overline{Barycentre Orthocentre} \, = \, " + distanceBarycentreOrthocentre
f = false
e = false
g = false
i = false
j = false
k = false
l = false

Tool: Bissectrices
Input: A, B, C
Output: Biss_1, Biss_2, Biss_3, BissIns, O_i

poly1, c, a, b = Polygon(A, B, C)
Biss_1 = AngularBisector(B, A, C)
Biss_2 = AngularBisector(C, B, A)
Biss_3 = AngularBisector(A, C, B)
O_i = Intersect(Biss_3, Biss_2)
h = OrthogonalLine(O_i, c)
D = Intersect(c, h)
BissIns = Circle(O_i, D)

Tool: Médiatrices
Input: A, B, C
Output: m1, m2, m3, O_c, mCirc

poly1, c, a, b = Polygon(A, B, C)
m2 = LineBisector(b)
m1 = LineBisector(a)
m3 = LineBisector(c)
O_c = Intersect(m2, m1)
mCirc = Circle(O_c, C)

Tool: Hauteurs
Input: A, B, C
Output: h1, h2, h3, Orthocentre

poly1, c, a, b = Polygon(A, B, C)
h1 = OrthogonalLine(A, a)
h3 = OrthogonalLine(C, c)
h2 = OrthogonalLine(B, b)
Orthocentre = Intersect(h1, h3)

Tool: Médianes
Input: A, B, C
Output: Méd_1, Méd_2, Méd_3, Barycentre

I_1 = Midpoint(C, B)
I_2 = Midpoint(A, B)
I_3 = Midpoint(A, C)
Méd_1 = Line(A, I_1)
Méd_3 = Line(C, I_2)
Méd_2 = Line(B, I_3)
Barycentre = Intersect(Méd_3, Méd_1)