Kružnica dotýkajúca sa polpriamok

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

Daný bod K

Zostrojenie bodu

p = AB

q = AC

os uhla ∡BAC

1. \; o: \text{ os uhla }∡BAC; \;  D∈o

D: na osi uhla

Kolmica na AB

Priesečník kolmice s AB

2.  \; k=(D, DE), \; E∈\overrightarrow{AB},DE⟂\overrightarrow{AB}

3.  \; F=AK∩k; \; FD

4. \; \mathscr{H}=(A, F→K)

5.  \; \mathscr{H}(D)=G

6.  \; k=(G,r=GK)

 \text{ Druhé riešenie nájdeme, ak použijeme priesečník }H  \text{ namiesto bodu }F.

K = (-4.81976, 2.53736)
C = (-9.10558, -2.7334)
B = (-9.55812, 5.62528)
A = (3.0191709090909162, 1.2942854545454587)
p = Ray(A, B)
q = Ray(A, C)
o = AngularBisector(C, A, B)
D = Point(o)
f = OrthogonalLine(D, p)
E = Intersect(f, p)
c = Circle(D, E)
g = Ray(A, K)
L = Intersect(c, g, 2)
F: L
h = Line(D, F)
i = Segment(D, F)
u = Vector(F, K)
j = Line(K, h)
G = Intersect(o, j)
k = Segment(G, K)
d = Circle(G, K)
T, I = Intersect(d, p)
T', J = Intersect(d, q)
H = Intersect(c, g, 1)