A

A

\textsf{Ist es möglich, den Kreis so zu platzieren, 
dass alle vier Eckpunkte des Vierecks\auf der Kreislinie liegen?\
Verschiebe dazu die \textcolor{#DB6114}{Kreise} am Mittelpunkt und ändere deren Größe mit Hilfe\des schwarzen Punktes.}

B

C

D

$\textsf{Neue Aufgabe}$

$\textsf{Lösung anzeigen}$

\textsf{Nicht möglich}

$\textsf{Neustart}$

A

D

C

B

C

B

A

D

B

A

D

C

A

D

C

B

\textsf{Möglich}

$\textsf{Möglich}

$\textsf{Möglich}

$\textsf{Möglich}

A

B

C

D

A

B

C

D

\textsf{Nicht möglich}

A

B

C

D

A

B

C

D

\textsf{Nicht möglich}

\textsf{Möglich}

$\textsf{Möglich}

\textsf\colorbox{ebe7f8}{Ein Umkreis berührt alle vier Eckpunkte des Vierecks.}

l2: {2, 3, 4, 1}
count = 1
l1: {3, 1, 2, 4}
randomNos = Shuffle(Sequence[Random[1, 3], i, 1, 100])
A_{2}: (-3, 1)
randomNos2 = Shuffle(Sequence[Random[1, 4], i, 1, 100])
num: l1(count)
num1: l2(count)
num2 = If(num ≟ num1, num1 + 1, num1)
H: (3, 1)
B: (0, 1)
C: (0, 3)
D: (-3, 3)
q1, d, c, b, a = Polygon(D, C, B, A_{2})
G: (6, 1)
F: (6, 4)
E: (3, 4)
q2, e, f, g, h = Polygon(E, F, G, H)
M: (-2, -3)
N = (-1, -3)
p = Circle(M, N)
M_{1}: (4, -3)
N_{1} = (5, -3)
p_1 = Circle(M_{1}, N_{1})
M_{2}: (10, -3)
N_{2} = (11, -3)
p_{2} = Circle(M_{2}, N_{2})
loesung = false
n = Segment(D, B)
q = Segment(C, A_{2})
r = Segment(E, G)
s = Segment(F, H)
O = Intersect(n, q)
P = Intersect(r, s)
t = Circle(O, B)
c_1 = Circle(P, G)
Q: (-2, -3)
R: (4, -3)
S: (10, -3)
T: (-1, -3)
U: (5, -3)
V: (11, -3)
W: M - N
W_1: M_{1} - N_{1}
W_2: M_{2} - N_{2}
I_{2} = (7.62, 1.44)
J = (9.12, 3.9)
K = (11.76, 3.84)
L = (11.5, 0.06)
q3, i, j, k, l = Polygon(I_{2}, J, K, L)
Z = (-0.84, 4.18)
A_1 = (-2.38, 1.46)
B_1: (6.78 - 10, 0.76)
C_1 = (-3.44, 3.22)
q4, z_1, a_1, b_1, m = Polygon(Z, A_1, B_1, C_1)
D_1 = (4.46, 1.42)
E_1 = (1.46, 0.04)
F_1 = (2.26, 3.64)
G_1 = (5.06, 3.82)
q5, d_1, e_1, f_1, g_1 = Polygon(D_1, E_1, F_1, G_1)
H_1 = (8.72, 1.64)
I_1 = (9.26, 3.92)
J_1 = (10.98, 3.38)
K_1 = (9.76, 2.98)
q6, h_1, i_1, j_1, k_1 = Polygon(H_1, I_1, J_1, K_1)
L_1 = Midpoint(A_{2}, B)
q_1 = Circle(S, V)
O_1 = (8.6, 0.52)
P_1: (11.32, 0.52)
Q_1: (11.32, 4.42)
R_1: (8.6, 4.42)
q7, r_1, l_1, p_{3}, o_1 = Polygon(R_1, Q_1, P_1, O_1)
m_1 = Segment(R_1, P_1)
n_1 = Segment(Q_1, O_1)
S_1 = Intersect(m_1, n_1)
s_1 = Circle(S_1, P_1)
I_4 = (1.66, 0.9)
U_1: (4.66, 0.9)
poly1, t_1, f_2, g_2, h_2, V_1, Z_1 = Polygon(I_4, U_1, 4)
i_2 = Segment(Z_1, U_1)
j_2 = Segment(V_1, I_4)
A = Intersect(i_2, j_2)
c_2 = Circle(A, U_1)
I = (-2, -3)
T_1 = (-1, -3)
d_2 = Circle(I, T_1)
B_2 = (8.8, 1.8)
C_2 = (10.36, 1.8)
poly2, k_2, l_2, m_2, n_2, D_2, E_2 = Polygon(B_2, C_2, 4)
q_2 = Segment(E_2, C_2)
r_2 = Segment(D_2, B_2)
F_2 = Intersect(q_2, r_2)
e_2 = Circle(F_2, C_2)
G_2: (4, -3)
H_2: (5, -3)
s_2 = Circle(G_2, H_2)
J_2: (-3.48, 0.7)
K_2: (-0.38, 0.7)
L_2: (-0.38, 2.1)
O_2 = (-3.48, 2.1)
q8, o_2, t_2, a_2, b_2 = Polygon(O_2, L_2, K_2, J_2)
f_3 = Segment(O_2, K_2)
g_3 = Segment(L_2, J_2)
P_2 = Intersect(f_3, g_3)
c_3 = Circle(P_2, K_2)
text11 = If(count ≟ 1 ∨ count ≟ (2 * "Neue Aufgabe"), "Nochmal!")
text12 = If(count ≟ 1 ∨ count ≟ (2 * "Neue Aufgabe"), "Nochmal!")
buttonText = If(count ≟ 1 ∨ count ≟ 2, "Neue Aufgabe", "Nochmal!")
buttonLatex: "\textsf{" + (LaTeX[buttonText]) + "}"
Q_2 = (-2, -3)
R_2 = (-1.18, -2.54)
bewegt = If(M ≠ (-2, -3) ∧ M_{1} ≠ (4, -3) ∧ M_{2} ≠ (10, -3), true, false)