$ Koostas: Maario \; Lemmik $
$ 12\; TJ : Koosinusteoreemi\;tõestus\;sõnadeta$

c^2=a^2+b^2-2·a·b·cosα

$Kommentaar:$
$kuskil\,on\; tõrge\; rööpkülikuga.$

A = (1.973106674869486, 9.136657391589535)
B = (20, 2)
C = (6.632075484388106, 2.088870060305771)
t1, c, a, b = Polygon(A, B, C)
a_{ruut}, f, g, h, i, D, E = Polygon(B, C, 4)
b_{ruut}, j, k, l, m, F, G = Polygon(C, A, 4)
c_{ruut}, n, p, q, r, H, I = Polygon(A, B, 4)
J = Midpoint(C, E)
s = Line(J, c)
t = Line(J, p)
K = Intersect(s, g)
L = Intersect(t, a)
M = Intersect(s, i)
N = Intersect(t, h)
q1, k_1, j_1, l_1, c_1 = Polygon(K, J, L, C)
q2, b_1, l_2, j_2, m_1 = Polygon(B, L, J, M)
q3, k_2, d, n_1, j_3 = Polygon(K, D, N, J)
q4, j_4, n_2, e, m_2 = Polygon(J, N, E, M)
u = Vector(J, A)
v = Vector(J, I)
w = Vector(J, H)
u_1 = Vector(J, B)
O = Centroid(q1)
P = Centroid(q2)
Q = Centroid(q3)
R = Centroid(q4)
O' = Translate(O, u_1)
P' = Translate(P, u)
Q' = Translate(Q, w)
R' = Translate(R, v)
f_1 = Segment(P, P')
g_1 = Segment(O, O')
h_1 = Segment(Q, Q')
i_1 = Segment(R, R')
T = Point(h_1)
U = Point(i_1)
V = Point(f_1)
S = Point(g_1)
v_1 = Vector(O, S)
w_1 = Vector(Q, T)
a_1 = Vector(R, U)
d_1 = Vector(P, V)
K' = Translate(K, v_1)
J' = Translate(J, v_1)
L' = Translate(L, v_1)
C' = Translate(C, v_1)
q1', k', j', l', c' = Polygon(K', J', L', C')
B' = Translate(B, d_1)
L'_{1} = Translate(L, d_1)
J'_{1} = Translate(J, d_1)
M' = Translate(M, d_1)
q2', b', l'_{1}, j'_{1}, m' = Polygon(B', L'_{1}, J'_{1}, M')
K'_{1} = Translate(K, w_1)
D' = Translate(D, w_1)
N' = Translate(N, w_1)
J'_{2} = Translate(J, w_1)
q3', k'_{1}, d', n', j'_{2} = Polygon(K'_{1}, D', N', J'_{2})
J'_{3} = Translate(J, a_1)
N'_{1} = Translate(N, a_1)
E' = Translate(E, a_1)
M'_{1} = Translate(M, a_1)
q4', j'_{3}, n'_{1}, e', m'_{1} = Polygon(J'_{3}, N'_{1}, E', M'_{1})
W = Midpoint(F, C)
Z = Centroid(c_{ruut})
p_1 = Segment(W, Z)
B_1 = Point(p_1)
e_1 = Vector(W, B_1)
q5 = Translate(b_{ruut}, e_1)
q_1 = Line(B, m)
r_1 = Line(G, a)
A_1 = Intersect(q_1, r_1)
s_1 = Segment(A_1, G)
C_1 = Point(s_1)
t_1 = Vector(A_1, B)
D_1 = Translate(C_1, t_1)
q6, g_2, c_2, f_2, h_2 = Polygon(G, C, D_1, C_1)
E_1 = Midpoint(C, C_1)
i_2 = Line(E_1, r)
F_1 = Intersect(i_2, a)
G_1 = Intersect(i_2, h_2)
q7, g_3, c_3, p_2, q_2 = Polygon(G, C, F_1, G_1)
q8, r_2, b_2, s_2, t_2 = Polygon(F_1, B, C_1, G_1)
H_1 = Centroid(q7)
I_1 = Centroid(q8)
J_1 = Intersect(n'_{1}, r)
K_1 = Intersect(d', p)
u_2 = Vector(F_1, J_1)
v_2 = Vector(F_1, K_1)
L_1 = Translate(I_1, u_2)
M_1 = Translate(H_1, v_2)
d_2 = Segment(H_1, M_1)
N_1 = Point(d_2)
w_2 = Vector(H_1, N_1)
G' = Translate(G, w_2)
C'_{1} = Translate(C, w_2)
P_1 = Translate(F_1, w_2)
Q_1 = Translate(G_1, w_2)
q7', g', c'_{1}, f_3, h_3 = Polygon(G', C'_{1}, P_1, Q_1)
V_1 = Intersect(m', c)
W_1 = Intersect(q, e')
q9, g_4, m_3, n_3, c_4 = Polygon(G, G_1, F_1, C)
q10, p_3, q_3, r_3, s_3 = Polygon(G_1, C_1, D_1, F_1)
B_2 = Intersect(q, k'_{1})
A_2 = Intersect(b', m')
C_2 = Point(c)
ümbermõõtt1 = Perimeter(t1)
Punktt1 = PointIn(t1)
β = Angle(B, C, A)
o: cos(β)
o_1: c^(2)
a_2: a^(2)
e_2: b^(2)
rööpkülik: (((2 * a) * b) * o)
väärtus_c: a_2 + e_2 - rööpkülik
tekst3: "" + (LaTeX[o_1]) + "=" + (LaTeX[a_2]) + "+" + (LaTeX[e_2]) + "-(" + (LaTeX[rööpkülik]) + ")=" + (LaTeX[väärtus_c]) + ""