Kružnica dotýkajúca sa polpriamok

 \text{ Zostrojte kružicu, ktorá sa dotýka polpriamok }p_1 = AB, p_2 = AC \text{ , pričom prechádza bodom }K.

Zostrojenie bodu

$\math {p = AB}$

$\math {q = AC}$

$\math {K}$

\text{Postup

$\mathcal o - \text{os uhla } \math∡BAC$

1. \; o\text{ - os uhla }∡BAC

2.  \; D \text{ na osi uhla}: D∈o

Kolmica na AB

Priesečník kolmice s AB

Kružnica [D, r = DE]

3. \; k' \text{ - kružnica dotýkajúca sa polpriamok}

4. \; F,H∈\overrightarrow{AK}∩k'

5. \; DF, DH

$\math G$

$\math G_1$

6.  \; G:\overleftrightarrow{KG}∥DF;  \; G_1:\overleftrightarrow{KG_1}∥DH; 

7.  \; k=(G,r=\left| GK \right| ; \; k_1=(G_1,r=\left| G_1K \right| 

A = (5.94682, 0.79738)
B = (-9.85578, 6.36338)
p = Ray(A, B)
C = (-8.52478, -3.75222)
q = Ray(A, C)
K = (-5.64498, -0.72722)
o_{1} = AngularBisector(C, A, B)
D = Point(o_{1})
f = OrthogonalLine(D, p)
E = Intersect(f, p)
k' = Circle(D, E)
o = Ray(A, K)
F = Intersect(k', o, 1)
H = Intersect(k', o, 2)
h = Line(D, F)
i = Segment(D, F)
g = Line(D, H)
l = Segment(D, H)
j = Line(K, h)
G = Intersect(o_{1}, j)
k_{2} = Segment(G, K)
m = Line(K, g)
G_1 = Intersect(m, o_{1})
n = Segment(K, G_1)
k = Circle(G, K)
T, I = Intersect(k, p)
T', J = Intersect(k, q)
k_1 = Circle(G_1, K)