3-4-5

sol 1

sol 2

sol 3

sol 4

sol 5

sol 6

toutes

détails

A = (-4, 2)
ab = Line(A, xAxis)
B = Point(ab)
c = Segment(A, B)
M = Midpoint(A, B)
mAB = LineBisector(A, B)
C_m = Rotate(B, 60°, A)
poly1 = Polygon(Join[{Sequence[Rotate[C_m, (5° * k), B], k, 1, 11], {A, M, C_m}}])
arc60 = CircleArc(B, C_m, A)
MC_m = Segment(C_m, M)
C = PointIn(poly1)
circ3 = Circle(A, (3 * c / 5))
circ4 = Circle(B, (4 * c / 5))
C_0 = Intersect(circ3, circ4, 1)
b = Segment(C, A)
a = Segment(C, B)
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
s1 = false
s2 = false
s3 = false
s4 = true
s5 = false
s6 = false
tt = true
mBC = LineBisector(C, B)
mAC = LineBisector(C, A)
d = false
Aα = Ray(A, Rotate[B, α - 90°, A])
Aβ = Ray(A, Rotate[B, β - 90°, A])
Aγ = Ray(A, Rotate[B, γ - 90°, A])
Ocα = Intersect(mAB, Aα)
Ocβ = Intersect(mAB, Aβ)
Ocγ = Intersect(Aγ, mAB)
Bα = Ray(B, Rotate[C, α - 90°, B])
Bβ = Ray(B, Rotate[C, β - 90°, B])
Bγ = Ray(B, Rotate[C, γ - 90°, B])
Oaβ = Intersect(mBC, Bβ)
Oaα = Intersect(mBC, Bα)
Oaγ = Intersect(Bγ, mBC)
Cα = Ray(C, Rotate[A, α - 90°, C])
Cβ = Ray(C, Rotate[A, β - 90°, C])
Cγ = Ray(C, Rotate[A, γ - 90°, C])
Obβ = Intersect(mAC, Cβ)
Obα = Intersect(mAC, Cα)
Obγ = Intersect(mAC, Cγ)
texte1: "a = " + a + "   b = " + b + "   c = " + c + ""
BC_1 = Segment(Obβ, Oaγ)
AC_1 = Segment(Oaγ, Ocα)
AB_1 = Segment(Ocα, Obβ)
ab_1 = Line(A, AB_1)
ac_1 = Line(B, AC_1)
bc_1 = Line(C, BC_1)
B''_1 = Intersect(ab_1, bc_1)
C''_1 = Intersect(ac_1, bc_1)
A''_1 = Intersect(ab_1, ac_1)
rc_1 = AffineRatio(A''_1, B''_1, A)
A'_1 = Dilate(B, rc_1, A)
ra_1 = AffineRatio(B''_1, C''_1, C)
C'_1 = Dilate(C, ra_1, B)
rb_1 = AffineRatio(C''_1, A''_1, B)
B'_1 = Dilate(A, rb_1, C)
ABC_1, a_1, b_1, c_1 = Polygon(B'_1, C'_1, A'_1)
texte2: "a' = " + a_1 + ""
Cx_1 = Ray(C, Rotate[B, (-β), C])
A_1a = Intersect(Cx_1, c)
Ax_1 = Ray(A_1a, Rotate[C, (-α), A_1a])
C_1a = Intersect(Ax_1, a)
c_1a = Segment(C, A_1a)
b_1a = Segment(A_1a, C_1a)
a_1a = Segment(C, C_1a)
texte3: "a' = " + a_1a + ""
BC_2 = Segment(Obγ, Oaβ)
AB_2 = Segment(Oaβ, Ocα)
AC_2 = Segment(Ocα, Obγ)
ab_2 = Line(B, AB_2)
ac_2 = Line(A, AC_2)
bc_2 = Line(C, BC_2)
C''_2 = Intersect(ac_2, bc_2)
A''_2 = Intersect(ab_2, ac_2)
B''_2 = Intersect(ab_2, bc_2)
rc_2 = AffineRatio(A''_2, B''_2, B)
ra_2 = AffineRatio(B''_2, C''_2, C)
rb_2 = AffineRatio(C''_2, A''_2, A)
B'_2 = Dilate(B, rc_2, A)
C'_2 = Dilate(C, ra_2, B)
A'_2 = Dilate(A, rb_2, C)
ABC_2, b_2, a_2, c_2 = Polygon(A'_2, C'_2, B'_2)
texte4: "a' = " + a_2 + ""
Cx_2 = Ray(C, Rotate[B, (-α), C])
B_2a = Intersect(Cx_2, c)
Bx_2 = Ray(B_2a, Rotate[C, (-β), B_2a])
C_2a = Intersect(a, Bx_2)
c_2a = Segment(C, B_2a)
a_2a = Segment(C_2a, B_2a)
b_2a = Segment(C, C_2a)
texte5: "a' = " + a_2a + ""
AC_3 = Segment(Obα, Oaγ)
BC_3 = Segment(Oaγ, Ocβ)
AB_3 = Segment(Ocβ, Obα)
ab_3 = Line(A, AB_3)
ac_3 = Line(C, AC_3)
bc_3 = Line(B, BC_3)
A''_3 = Intersect(ab_3, ac_3)
C''_3 = Intersect(ac_3, bc_3)
B''_3 = Intersect(ab_3, bc_3)
rc_3 = AffineRatio(A''_3, B''_3, A)
ra_3 = AffineRatio(B''_3, C''_3, B)
rb_3 = AffineRatio(C''_3, A''_3, C)
A'_3 = Dilate(B, rc_3, A)
B'_3 = Dilate(C, ra_3, B)
C'_3 = Dilate(A, rb_3, C)
ABC_3, c_3, a_3, b_3 = Polygon(A'_3, B'_3, C'_3)
Cx3 = Ray(C, Rotate[A, β, C])
A_3a = Intersect(Cx3, c)
Ax3 = Ray(A_3a, Rotate[C, α, A_3a])
C_3a = Intersect(Ax3, b)
c_3a = Segment(C, A_3a)
b_3a = Segment(A_3a, C_3a)
a_3a = Segment(C_3a, C)
texte7: "a' = " + a_3 + ""
texte6: "a' = " + a_3a + ""
AB_4 = Segment(Oaα, Ocβ)
BC_4 = Segment(Ocβ, Obγ)
AC_4 = Segment(Obγ, Oaα)
ac_4 = Line(C, AC_4)
bc_4 = Line(A, BC_4)
ab_4 = Line(B, AB_4)
A''_4 = Intersect(ac_4, ab_4)
C''_4 = Intersect(ac_4, bc_4)
B''_4 = Intersect(bc_4, ab_4)
rc_4 = AffineRatio(A''_4, B''_4, B)
ra_4 = AffineRatio(B''_4, C''_4, A)
rb_4 = AffineRatio(C''_4, A''_4, C)
B'_4 = Dilate(B, rc_4, A)
A'_4 = Dilate(C, ra_4, B)
C'_4 = Dilate(A, rb_4, C)
ABC_4, b_4, c_4, a_4 = Polygon(C'_4, A'_4, B'_4)
Cx_4 = Ray(C, Rotate[A, α, C])
B_4a = Intersect(Cx_4, c)
Bx_4 = Ray(B_4a, Rotate[C, β, B_4a])
C_4a = Intersect(Bx_4, b)
c_4a = Segment(C, B_4a)
a_4a = Segment(C_4a, B_4a)
b_4a = Segment(C_4a, C)
texte8: "a' = " + a_4 + ""
texte9: "a' = " + a_4a + ""
AB_{5} = Segment(Obα, Oaβ)
BC_{5} = Segment(Oaβ, Ocγ)
AC_{5} = Segment(Ocγ, Obα)
ac_5 = Line(A, AC_{5})
bc_5 = Line(B, BC_{5})
ab_5 = Line(C, AB_{5})
A''_5 = Intersect(ac_5, ab_5)
C''_5 = Intersect(ac_5, bc_5)
B''_5 = Intersect(bc_5, ab_5)
rc_5 = AffineRatio(A''_5, B''_5, C)
ra_5 = AffineRatio(B''_5, C''_5, B)
rb_5 = AffineRatio(C''_5, A''_5, A)
C'_5 = Dilate(B, rc_5, A)
B'_5 = Dilate(C, ra_5, B)
A'_5 = Dilate(A, rb_5, C)
ABC_5, c_5, a_5, b_5 = Polygon(A'_5, B'_5, C'_5)
Cx_5 = Ray(C, Rotate[A, β, C])
C_5a = Intersect(Cx_5, c)
a_5a = Segment(C, C_5a)
b_5a = Segment(C_5a, A)
c_5a = Segment(A, C)
texte10: "a' = " + a_5 + ""
texte11: "a' = " + a_5a + ""
AB_6 = Segment(Oaα, Obβ)
AC_6 = Segment(Oaα, Ocγ)
BC_6 = Segment(Ocγ, Obβ)
ac_6 = Line(B, AC_6)
bc_6 = Line(A, BC_6)
ab_6 = Line(C, AB_6)
A''_6 = Intersect(ac_6, ab_6)
C''_6 = Intersect(ac_6, bc_6)
B''_6 = Intersect(bc_6, ab_6)
B'_6 = Midpoint(C, A)
C'_6 = Midpoint(A, B)
A'_6 = Midpoint(B, C)
ABC_6, c_6, b_6, a_6 = Polygon(B'_6, A'_6, C'_6)
texte12: "a' = " + a_6 + ""
aγ = CircleArc(Oaγ, B, C)
bβ = CircleArc(Obβ, C, A)
cα = CircleArc(Ocα, A, B)
bγ = CircleArc(Obγ, C, A)
aβ = CircleArc(Oaβ, B, C)
bα = CircleArc(Obα, C, A)
cβ = CircleArc(Ocβ, A, B)
aα = CircleArc(Oaα, B, C)
cγ = CircleArc(Ocγ, A, B)