x_{1,2}

A_1

B_1

C_1

D_1

E_1

V_1

V_2

A_2

B_2

C_2

D_2

E_2

a_2

a_1

P_2

P_1

R_2

R_1

P_2'

P_1'

r_1

r_2

p_1^\rho

I

II

X_1

Y_1

I'

II'

X_2

Y_2

\textrm{Sestrojte průsečíky přímky }a\textrm{ s kolmým jehlanem, jehož podstavou je pravidelný pětiúhelník }ABCDE\textrm{ ležící v půdorysně.}

X_1 = Point(xAxis)
X_2 = Point(xAxis)
a = Segment(X_1, X_2)
A_1 = Point(yAxis)
V_1 = Point(yAxis)
b = Segment(A_1, V_1)
B_1 = Rotate(A_1, 72°, V_1)
α = Angle(A_1, V_1, B_1)
C_1 = Rotate(B_1, 72°, V_1)
β = Angle(B_1, V_1, C_1)
D_1 = Rotate(C_1, 72°, V_1)
γ = Angle(C_1, V_1, D_1)
E_1 = Rotate(D_1, 72°, V_1)
δ = Angle(D_1, V_1, E_1)
c = Segment(B_1, V_1)
d = Segment(V_1, C_1)
e = Segment(C_1, D_1)
f = Segment(V_1, D_1)
g = Segment(V_1, E_1)
h = Segment(A_1, E_1)
i = Segment(E_1, D_1)
j = Segment(A_1, B_1)
k = Segment(C_1, B_1)
pos = 13 (slider from 0 to 13, step 1)
l = OrthogonalLine(A_1, a)
m = OrthogonalLine(E_1, a)
n = OrthogonalLine(B_1, a)
p = OrthogonalLine(C_1, a)
q = OrthogonalLine(D_1, a)
B_2 = Intersect(n, a)
C_2 = Intersect(p, a)
A_2 = Intersect(l, a)
D_2 = Intersect(q, a)
E_2 = Intersect(m, a)
V_2 = Point(l)
r = Segment(B_2, V_2)
s = Segment(C_2, V_2)
t = Segment(A_2, V_2)
a_1 = Segment(D_2, V_2)
b_1 = Segment(E_2, V_2)
P_2 = Point(a)
X_4 = (-3.34, 3.96)
c_1 = Segment(P_2, X_4)
X_5 = (4.28, -2.66)
X_6 = (-4.92, -4.14)
d_1 = Segment(X_5, X_6)
e_1 = OrthogonalLine(P_2, a)
P_1 = Intersect(d_1, e_1)
f_1 = Segment(P_2, P_1)
R_2 = Point(c_1)
g_1 = OrthogonalLine(R_2, a)
R_1 = Intersect(d_1, g_1)
h_1 = Segment(R_2, R_1)
i_1 = Ray(V_2, R_2)
j_1 = Ray(V_1, R_1)
P_2' = Intersect(a, i_1)
k_1 = Segment(V_2, P_2')
l_1 = OrthogonalLine(P_2', a)
P_1' = Intersect(j_1, l_1)
X_7 = Point(j_1)
m_1 = Segment(V_1, X_7)
n_1 = Segment(P_2', P_1')
p_1 = Segment(P_1', P_1)
M_1 = Intersect(p_1, k)
N_1 = Intersect(p_1, i)
q_1 = Segment(P_1', M_1)
r_1 = Segment(M_1, N_1)
s_1 = Segment(N_1, P_1)
t_1 = Segment(M_1, V_1)
a_2 = Segment(V_1, N_1)
X = Intersect(d_1, t_1)
Y = Intersect(d_1, a_2)
b_2 = Segment(X_6, X)
c_2 = Segment(X, Y)
d_2 = Segment(Y, P_1)
e_2 = Segment(P_1, X_5)
mnohoúhelník1, v_1, m_2, n_2 = Polygon(M_1, N_1, V_1)
f_2 = OrthogonalLine(N_1, a)
g_2 = OrthogonalLine(M_1, a)
M_2 = Intersect(g_2, a)
N_2 = Intersect(f_2, a)
h_2 = Segment(M_2, V_2)
i_2 = Segment(N_2, V_2)
X' = Intersect(h_2, c_1)
Y' = Intersect(i_2, c_1)
j_2 = Segment(X_4, X')
k_2 = Segment(X', Y')
l_2 = Segment(Y', P_2)
mnohoúhelník2, v_2, m_3, n_3 = Polygon(M_2, N_2, V_2)
p_2 = Segment(Y, Y')
q_2 = Segment(X, X')