b

v_c

náčrtek

Zelené\ objekty\ známe\

B

a

C

a

Sestrojte\ ΔABC,znáte-li:\a,b, v_c

b

v_c

P

Poraď

udělej

zpět

velikosti úseček

A

A'

vynuluj

Popis konstrukce

∅⇔((a > v_c) ∧ (b < v_c)) ∨(a ≤ v_c)\
∃!\ řešení⇔((a > v_c) ∧ (b = v_c)) ∨(a=b>v_c)\ 
(a > v_c) ∧ (b > v_c) ⇒ ∃\ 2\ řešení

Podmínky řešitelnosti a počet řešení

A = (-4.4, 3.32)
B = (-1.12, 4.08)
C = (-2.92, 5.48)
mnohoúhelník1, c, a, b_1 = Polygon(A, B, C)
f = OrthogonalLine(C, c)
P = Intersect(f, c)
v_1 = Segment(C, P)
d = false
D = (2.64, -1.16)
d_a = 4.7 (slider from 0 to 8, step 0.1)
E = Point(Circle[D, d_a])
g = Segment(D, E)
τ = Semicircle(D, E)
d_b = 3.8 (slider from 0 to 8, step 0.1)
d_{v_c} = 2.9 (slider from 0 to 8, step 0.1)
k = Circle(E, d_{v_c})
F = Intersect(τ, k, 1)
l = -5 (slider from -5 to 50, step 1)
text4: "Body\ " + (Name[B]) + "," + (Name[P]) + ", " + (Name[A]) + "\ jsou\ na\ stejné\ úsečce\\⇒nejprve\ vytvoř\ Δ" + (Name[C]) + "" + (Name[P]) + "" + (Name[B]) + ""
m = false
text3: "Bod\ " + (Name[P]) + "\ je\ pata\ výšky, úhel\ " + (Name[C]) + "" + (Name[P]) + "" + (Name[B]) + "\ má\ 90°\\vytvoř\ thaletovu\ kružnici\ nad\ " + (Name[B]) + "" + (Name[C]) + ""
text5: "Bod\ " + (Name[P]) + "\ má\ od\ bodu\ " + (Name[C]) + "\ známou\ vzdálenost\left(" + (LaTeX[d_{v_c}]) + " \right)"
v_c = Segment(E, F)
text6: "Bod\ " + (Name[A]) + "\ leží\ na\ jedné\ úsečce\ jako\ " + (Name[B]) + "\ a\ " + (Name[P]) + ""
h = Line(D, F)
text7: "Bod\ " + (Name[A]) + "\ leží\ ve\ známé\ vzdálenosti\ od\ bodu\ " + (Name[B]) + "\ \left(" + (LaTeX[d_b]) + "\right) "
p = Circle(E, d_b)
G, H = Intersect(p, h)
mnohoúhelník2, e, g_1, d_1 = Polygon(G, D, E)
mnohoúhelník3, e_1, h_1, d_2 = Polygon(H, D, E)
b' = Segment(E, G)
b = Segment(E, H)
i = false
text8: "1.\ Úsečka\ " + (Name[B]) + "" + (Name[C]) + ";\ \left|" + (Name[B]) + " " + (Name[C]) + " \right| =" + (Name[a]) + "\left( nyní\ " + (LaTeX[d_a]) + "  \right) \\2.\ Thaletova\ kružnice\ nad\ " + (Name[B]) + "" + (Name[C]) + "\\3.\ k;\ k\left( " + (Name[C]) + "," + (Name[v_c]) + "\left( nyní\ " + (LaTeX[v_c]) + "  \right)   \right) \\4.\ " + (Name[P]) + ";" + (Name[P]) + "∈" + (Name[k]) + "∩" + (Name[τ]) + "\\5.\ " + (Name[h]) + ";" + (Name[B]) + "∈" + (Name[h]) + "∧" + (Name[P]) + "∈" + (Name[h]) + "\\6.\ p;\ p(" + (Name[C]) + ";" + (Name[b]) + "\ (nyní\ " + (LaTeX[d_b]) + "))\\7.\ " + (Name[A]) + ";" + (Name[A]) + "∈" + (Name[p]) + "∩" + (Name[h]) + "\\8.\ Δ" + (Name[A]) + "" + (Name[B]) + "" + (Name[C]) + ""
j = false