$S$

1.  \; k=(S, r=7); M∈k_1(S, r_1=11)

$M$

$A$

$B$

$T$

2.  \text{ Mocnosť: }MA×MB=MT^2

3.  \text{ Predpoklad: }MA×MB=d×2d=2d^2=MT^2

$d$

$d$

4.  \text{ Pytagoras: }MT^2+ST^2=MS^2

5.  \text{ Dosadením: }2d^2+7^2=11^2⇒\mathbf\red {d=6}

6.   \; ω=(M, r_ω=6); \; K=ω \; ∩ \; k;  \; L=\overrightarrow{MK}∩k

$K$

$L$

7.  \text{ Zrejme: }MK×ML=MT^2 \; (6×12=72)

\text{Pohybujte bodom }M.

S = (1.44, -0.24)
c = Circle(S, 7)
d = Circle(S, 11)
M = Point(d)
A = Point(c)
s = Ray(M, A)
B = Intersect(c, s, 2)
f, g = Tangent(M, c)
T = Intersect(c, g)
h = Segment(M, A)
i = Segment(A, B)
t1, t, m, s_1 = Polygon(M, S, T)
ω = Circle(M, 6)
C = Intersect(c, ω, 2)
j = Ray(M, C)
D = Intersect(c, j, 2)