Zostrojte trojuholník ak je dané: strana a, ťažnica t_c, uhol α =∢CAB. 

Logický rozbor - analýza

kroky 1 až 4

Rozbor

Konštrukcia

Postup konštrukcie

a

2. Bod A ∈ k(S, r = SA), z ktorej vidieť t_c pod uhlom α

3. Bod B ∈ k´ ∩ m, (k´ súmerná cez C_1) a m(C, polomer = a)

od kroku 5

a

α

t_c

C

C_1

t_c

S

k

3. Zostrojme 

     a: oblúk k, z ktorého vidieť t_c pod uhlom α 

     b: oblúk k' stredovo súmerný s kružnicou k podľa C_1

k'

m

5. B ∈ k' ∩ m

B

6. Bod A bude stredovo súmerný s B podľa C_1

A

Trojuholník ABC

a

α

roz = false
kon = false
A = (-1.4615378250000004, -0.5084380069999999)
B = (8.538462174999996, -0.5084380069999999)
C = (6.538462174999999, 5.4915619929999995)
t1, c, a, b = Polygon(A, B, C)
C_1 = Midpoint(A, B)
t_c = Segment(C, C_1)
g = Segment(C, B)
α = Angle(C, A, B)
text3: "1. Vyznačme dané prvky: a = " + a + ", t_c = " + t_c + ", α = " + α + ""
f = Ray(C, C_1)
F = Midpoint(C_1, C)
C' = Rotate(C, (-α), C_1)
β = Angle(C', C_1, C)
h = Line(C_1, C')
i = OrthogonalLine(C_1, h)
j = OrthogonalLine(F, f)
S = Intersect(i, j)
k = Circle(S, A)
k' = Mirror(k, C_1)
p = Circle(C, a)
d_1 = 8 (slider from 1 to 10, step 0.1)
γ = 0.5235987755982988 rad (slider from 0 to 90°, step 0.017453292519943295)
e = 6 (slider from 1 to 10, step 0.1)
text7: "1. Zvoľme posuvníky: a = " + d_1 + ", t_c = " + e + ", α = " + γ + ""
text8: "2. Zvoľme body C, C_1 tak, aby t_c = CC_1 = " + e + ""
D = (6, 6)
L = (-0.8670449934000015, -2.9780847550000176)
l = Ray(D, L)
q = Circle(C, e)
E = Intersect(q, l, 1)
m = Segment(D, E)
G = Midpoint(E, D)
n = OrthogonalLine(G, l)
D' = Rotate(D, (-γ), E)
δ = Angle(D', E, D)
r = Ray(E, D')
s = OrthogonalLine(E, r)
H = Intersect(n, s)
I = Intersect(r, s)
t = CircleArc(H, D, E)
t' = Mirror(t, E)
text13: "4. Zostrojme kružnicu m(C, r = " + d_1 + ")"
c_1 = Circle(D, d_1)
J, K = Intersect(c_1, t')
J' = Mirror(J, E)
t2, d_2, j', j_1 = Polygon(J', J, D)
ε = Angle(D, J', J)