3

6

4 řešení

a = 6
b = 5
v_a = 3
A = (5.241726438055262, 19.068985200456748)
C = Point(Circle[A, b])
d_1 = Segment(A, C)
e_1 = Semicircle(C, A)
k_T = Semicircle(A, C)
S = Midpoint(A, C)
g_1 = Circle(A, v_a)
C_1 = Point(g_1)
v = Vector(A, C_1)
D = Midpoint(A, C_1)
A_1 = Intersect(e_1, g_1, 1)
j_1 = Line(A_1, C)
A_2 = Intersect(k_T, g_1, 1)
c = Segment(A, A_2)
d = Segment(A_2, C)
e = Segment(A_1, C)
f = Segment(A_1, A)
α = Angle(C, A_1, A)
β = Angle(A, A_2, C)
n_1 = Line(C, A)
g = Line(A_1, C)
h = Line(A_2, C)
B = Point(g)
E = Point(g)
F = Point(h)
G = Point(h)
i = Segment(B, E)
j = Segment(F, G)
k = Circle(C, a)
H = Point(k)
u = Vector(C, H)
I = Midpoint(C, H)
V = Point(n_1)
W = Point(n_1)
Z = Point(j_1)
D_1 = Point(j_1)
B_1 = Intersect(k, i, 1)
B_4 = Intersect(k, j, 1)
B_2 = Intersect(k, i, 2)
B_3 = Intersect(k, j, 2)
poly1, a_1, b_1, c_1 = Polygon(B_1, C, A)
poly2, c_2, a_2, b_4 = Polygon(A, B_4, C)
poly3, b_3, a_3, c_3 = Polygon(A, C, B_3)
poly4, b_2, a_4, c_4 = Polygon(A, C, B_2)

Tool: Zlatý řez 1 (command Zlatýřez1)
Input: A, B
Output: F

a = Segment(A, B)
b = OrthogonalLine(B, a)
C = Midpoint(B, A)
c = Circle(B, C)
D = Intersect(c, b, 2)
d = Segment(A, D)
e = Circle(D, B)
E = Intersect(e, d, 1)
f = Circle(A, E)
F = Intersect(f, a, 1)

Tool: Zlatý řez 2 (command Zlatýřez2)
Input: A, B
Output: F

a = Ray(A, B)
c = OrthogonalLine(B, a)
e = Circle(B, A)
C = Midpoint(A, B)
D, E = Intersect(e, c)
f = Circle(C, E)
F = Intersect(f, a, 1)

Tool: Zlatý řez 3 (command Zlatýřez3)
Input: D, E
Output: F'

F = Zlatýřez2(D, E)
v = Vector(D, E)
F' = Translate(F, v)

Tool: nabrat poloměr (command nabratpoloměr)
Bod, bod, střed
Input: A, B, C
Output: g

u = Vector(A, B)
C' = Translate(C, u)
g = Circle(C, C')

Tool: obdélník ze 3 bodů (command obdélníkze3bodů)
Input: A, B, C
Output: b_1, a_1, d_1, e

a = Segment(A, B)
b = OrthogonalLine(B, a)
c = Line(C, a)
D = Intersect(b, c)
d = OrthogonalLine(A, a)
E = Intersect(c, d)
poly1, a_1, b_1, d_1, e = Polygon(A, B, D, E)

Tool: odpichovátko
Input: A, B, C
Output: C'

u = Vector(A, B)
C' = Translate(C, u)

Tool: přenesení úsečky (command přeneseníúsečky)
Input: A, B, C
Output: a, C'

u = Vector(A, B)
C' = Translate(C, u)
a = Segment(C, C')

Tool: zlatý trojúhelník1 (command zlatýtrojúhelník1)
Input: A, B
Output: b, a, e, F

a = Segment(A, B)
C = Zlatýřez2(B, A)
D = Zlatýřez2(A, B)
c = Circle(B, C)
d = Circle(A, D)
E, F = Intersect(c, d)
b = Segment(A, F)
e = Segment(B, F)

Tool: zlatý trojúhelník 2 (command zlatýtrojúhelník2)
Input: A, B
Output: a, h, i, G

a = Segment(A, B)
C = Zlatýřez2(B, A)
D = Zlatýřez2(A, B)
f = Circle(A, C)
g = Circle(B, D)
G, H = Intersect(f, g)
h = Segment(A, G)
i = Segment(B, G)

Tool: kruhova_inverze
poloměr, střed, vzor
Input: r, S, A
Output: A', A_1, k, l, c

c = Circle(S, r)
a = Ray(S, A)
b = OrthogonalLine(A, a)
B, C = Intersect(c, b)
d = Segment(S, C)
e = OrthogonalLine(C, d)
A' = Intersect(a, e)
f, g = Tangent(A, c)
E = Intersect(c, f, 1)
i = OrthogonalLine(E, a)
A_1 = Intersect(a, i)
k = Segment(S, A')
l = Segment(S, A)

Tool: ekvidistanta
2 body na přímce a vzdálenost
Input: A, B, r
Output: e, f

a = Line(A, B)
b = OrthogonalLine(A, a)
d = Circle(A, r)
C = Intersect(d, b, 2)
e = OrthogonalLine(C, b)
D = Intersect(d, b, 1)
f = OrthogonalLine(D, b)