\; \text{Dokážte, že os uhla } ∡BAC \text{ a os protiľahlej strany }BC \text{ sa pretínajú na opísanej kružnici }k(ABC)

 \text{Postup} 

$\math o_α$

1.  \; \text{Nech } D=o_α∩k \text{, potom oblúky }\widehat{BD}≅\widehat{DC}

2.  \; \text{ Odkiaľ  } \overleftrightarrow{DS} \; ⟂ \; AB \text{ (tetiva)}

3.  \; \text{ Preto musí stred } A_1∈\overleftrightarrow{SD}⇒D∈\overleftrightarrow{SA_1}

4.  \; \text{Záver: os }o_a\text{ strany } BC \text{ prechádza bodom }D.

5.  \; \text{ ... } a,b \text{ ... }

A = (2.999411321333412, 1.6939037264044465)
B = (8.352002868199314, 1.708331196881174)
C = (7.500782110072391, 7.306189741851444)
t1, c, a, b = Polygon(A, B, C)
k = Circle(A, B, C)
S = Center(k)
f, g = AngularBisector(b, c)
D = Intersect(k, g, 2)
d = CircleArc(S, B, D)
e = CircleArc(S, D, C)
h = Line(D, S)
A_1 = Midpoint(B, C)