Kružnica dotýkajúca sa polpriamok

 \text{ Zostrojte kružicu, ktorá sa dotýka polpriamok }p = AB,q = AC \text{ a danej kružnice }k.

$\mathit {A}$

$\mathit {B}$

$\mathit {p = AB}$

$\mathit {C}$

$\mathit {q = AC}$

$\mathcal {S}$

\text{Využijeme rovnoľahlosť }\mathscr{H}=(T, κ)

\text{Postup

1. \;\text{Dotyčnice }t_1,t_2,t'_1,t'_2\text{ ku }k \text{ rovnobežné s }p,q

2.  \; P_1=t_1∩t_2; \; P'_1=t'_1∩t'_2; 

3. \; p=\overleftrightarrow{AP_1}; \; p'=\overleftrightarrow{AP'_1}

4. \; P,Q∈p∩k; \; P',Q'∈p'∩k

5. \; O_p,∈o∩\overleftrightarrow{PS}; \; O_q∈o∩\overleftrightarrow{QS}; o\text{ - os uhla }∡BAC

6. \; \text{Kružnice }k_1(O_p,\left|  O_pP\right| ); k_2(O_q,\left|  O_qQ\right| )

7. \; \text{Kružnice }k_1(O'_p,\left|  O_pP'\right| ); k_2(O_q,\left|  O_qQ'\right| )

r = 3.1 (slider from 1 to 8, step 0.1)
A = (3.26, 2.64)
B = (-16.12612, 9.38308)
p = Ray(A, B)
C = (-14.28934, -5.15144)
q = Ray(A, C)
S = (-11.25466, 1.0244)
c = Circle(S, r)
f = OrthogonalLine(S, p)
h = OrthogonalLine(S, q)
D = Intersect(c, f, 1)
t_1 = OrthogonalLine(D, f)
F = Intersect(c, h, 2)
t_2 = OrthogonalLine(F, h)
K = Intersect(c, f, 2)
L = Intersect(c, h, 1)
t'_2 = OrthogonalLine(L, h)
t'_1 = OrthogonalLine(K, f)
P_1 = Intersect(t_1, t_2)
P'_1 = Intersect(t'_2, t'_1)
j = Line(A, P_1)
t = Line(A, P'_1)
P, Q = Intersect(c, j)
P' = Intersect(c, t, 1)
Q' = Intersect(c, t, 2)
l = Line(S, P)
m = Line(S, Q)
o, g = AngularBisector(p, q)
O_{p} = Intersect(o, l)
O_{q} = Intersect(m, o)
e = Circle(O_{q}, Q)
d = Circle(O_{p}, P)
a = Line(P', S)
b = Line(S, Q')
O'_q = Intersect(o, b)
c_1 = Circle(O'_q, Q')
O'_p = Intersect(a, o)
d_1 = Circle(O'_p, P')