\text{Zostrojte } \triangle ABC, \text{ ak je dané } ∡A=α, ∡B=β, \text{ a obvod }o=a+b+c

\text{ Rozbor úlohy

\text{ Nech }\triangle ABC \text{ je hľadaný trojuholník

\text{ Zvoľme }P∈\overrightarrow{AB},Q∈\overrightarrow{BA} : |AP|=c, |BQ|=a

P

\text{ Trojuholníky }\triangle PCA,\triangle QCB,   \text{ sú rovnoramenné

\text{ Osi ich základní prehádzajú vrcholmi }A, B

\text{ Zrejme } ∡APC=\frac{1}{2} ∡BAC,∡QBC=\frac{1}{2} ∡ABC

\text{ Konštrukciu začneme úsečkou }PQ= o 

\text{ Pokračujeme uhlami }∡P=\frac{α}{2}, ∡Q=\frac{β}{2}⇒\text{ bod }C

\text{ Osi úsečiek }PC, QC ⇒\text{ body }A,B

P = (0, 2)
α = 0.6632251157578453 rad (slider from 0 to 180°, step 0.017453292519943295)
β = 1.0471975511965976 rad (slider from 0 to 180°, step 0.017453292519943295)
o = 10.2 (slider from 4 to 20, step 0.1)
Q_{1} = Point(Circle[P, o])
f = Segment(P, Q_{1})
Q' = Rotate(Q_{1}, α / 2, P)
γ = Angle(Q_{1}, P, Q')
P' = Rotate(P, β / 2, Q_{1})
P'_{1} = Rotate(P, (-(β / 2)), Q_{1})
δ = Angle(P'_{1}, Q_{1}, P)
g = Ray(P, Q')
h = Ray(Q_{1}, P'_{1})
C = Intersect(g, h)
i = LineBisector(P, C)
j = LineBisector(C, Q_{1})
A = Intersect(i, f)
B = Intersect(j, f)
t1, c, a, b = Polygon(A, B, C)
ε = Angle(B, A, C)
ζ = Angle(A, B, C)
k = Line(A, B)
d = Circle(A, C)
D, E = Intersect(d, k)
l = Segment(A, D)
m = Segment(A, C)
e = Circle(B, C)
Q = Intersect(e, k, 2)
n = Segment(B, C)
p = Segment(B, Q)
t2, a_1, d_1, c_1 = Polygon(D, C, A)
t3, b_1, q, c_2 = Polygon(Q, C, B)
r = LineBisector(D, C)
s = LineBisector(C, Q)
η = Angle(A, D, C)
θ = Angle(B, Q, C)