\text{Zostrojte }\triangle ABC: a:b=4:5,γ,v_c

 \text{Rozbor} 

1.  \text{ Zostrojme (rovnoľahlý) }\triangle A'B'C: a=5j,b=4j,γ

γ

\left| A'C \right|  =5j

\left| B'C \right| =4j

2.  \; \text{Nech }v'_c \text{  je výška v }\triangle A'B'C

4. \; \mathscr{H}(A')=A;  \;  \; \mathscr{H}(B')=B

v_c = 6 (slider from 1 to 10, step 0.1)
γ = 1.2740903539558606 rad (slider from 0 to 180°, step 0.017453292519943295)
A' = (3.455845228775321, 3.6349521047154925)
C = (8, 7)
f = Ray(C, A')
A'_{1} = Rotate(A', γ, C)
β = Angle(A', C, A'_{1})
g = Ray(C, A'_{1})
vzdialenosťAC = Distance(A', C)
Midpoint(A', C)
c = Circle(C, (4 / 5 * Distance[A', C]))
B' = Intersect(c, g, 1)
vzdialenosťCB' = Distance(C, B')
Midpoint(C, B')
TextCB': Name[C] + (Name[B']) + " = " + vzdialenosťCB'
vzdialenosťA'C = Distance(A', C)
h = Line(A', B')
i = OrthogonalLine(C, h)
C'_1 = Intersect(h, i)
v'_c = Segment(C'_1, C)
d = Circle(C, v_c)
C_1 = Intersect(d, i, 1)
text3: "3.  \; \text{ V rovnoľahlosti } \mathscr{H}\left( C,κ=\frac{v_c}{v'_c}=\frac{" + (LaTeX[v_c]) + " }{" + (LaTeX[v'_c]) + " }  \right) : \mathscr{H}(C'_1)=C_1"
Midpoint(A', C)
j = Line(C_1, h)
A = Intersect(j, f)
B = Intersect(j, g)
t1, c_1, a, b = Polygon(A, B, C)
vzdialenosťCC1 = Distance(C, C_1)
Midpoint(C, C_1)
TextCC1: "\left| CC_1 \right| = " + (LaTeX[vzdialenosťCC1]) + ""
k = Segment(C, C_1)
Midpoint(C, B')