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

c

\text{Posuňme }BC →B'C' \text{ o vektor a + b 

| BB'| =| CC'|=a+b

\triangle AMC, \triangle B'MC'\text{  rovnoramenné: } AC≅CM; B'C'≅C'M

CM∥AB⇒∡ANC≅MAB⇒AM \text\red{ je os uhla}.

\overleftrightarrow{AM}, \overleftrightarrow{B'M} \text{ sú osi uhlov } ∡A=α,∡B'=β

\text{ Postup}

1.  \; AB'=PQ=o

2.  \overleftrightarrow{AM}, \overleftrightarrow{B'M} \text{ ramená uhlov } \frac{α}{2},\frac{β}{2}

3.  \; C:CS∥AB'→B:CB∥C'B'

A = (2, -4)
B = (6, -4)
α = 0.6981317007977318 rad (slider from 0 to 180°, step 0.017453292519943295)
β = 1.0471975511965976 rad (slider from 0 to 180°, step 0.017453292519943295)
A'_{2} = Rotate(A, (-β), B)
i = Ray(B, A'_{2})
M' = Rotate(B, α, A)
g = Ray(A, M')
C = Intersect(g, i)
f = Ray(A, B)
t1, c_1, a, b = Polygon(A, B, C)
γ = Angle(B, A, M')
δ = Angle(A'_{2}, B, A)
P = (1.0327272727272772, -6.001818181818183)
D = (17, -6)
h = Ray(P, D)
c = Circle(P, Segment[A, B])
E = Intersect(c, h, 1)
d = Circle(E, Segment[B, C])
F = Intersect(d, h, 2)
e = Circle(F, Segment[C, A])
Q = Intersect(e, h, 2)
j = Segment(P, E)
v = Vector(E, Q)
B' = Translate(B, v)
C' = Translate(C, v)
a' = Segment(B', C')
p = Circle(C', B')
k = Circle(C, A)
M = Intersect(k, p)
l = Segment(C, C')
m = Segment(B, B')
t2, c_2, a_1, h_1 = Polygon(A, M, C)
t3, c', b', h_2 = Polygon(B', M, C')