Trojúhelník A_1B_1C_1

Polopřímka →C_2P a vznik bodu A_2

Polopřímka →C_1P a vznik bodu A_1

Polopřímka →C_1Q a vznik bodu B_1

Polopřímka →C_2Q a vznik bodu B_2

Trojúhelník A_2B_2C_2

Použití bodu C_1

Použití bodu C_2

Prúsečíky Tk_{PQ} a k

Thaletova kružnice nad PQ

Postup

Je\, dána\, kružnice\, k\, a\, uvnitř\, ní\, body\, P,\,Q. \
Vepiště\, do \, kružnice\, pravoúhlý\, trojúhelník\, ABC\, tak,\,\
aby\, bod\, P\,\, ležel\, na\, odvěsně\, AC\, a\, bod\, Q\, na\, odvěsně\, BC.

Zadání

Diskuze:\
\,\,\,S...střed\, kružnice\, k\
\,\,\,S_{PQ}...střed\, úsečky\, PQ\
_{........................................................}\
\,\,\,r_k-∣SS_{PQ}∣≟ ∣PS_{PQ}∣:\
\,\,\,\,\,\,\,∙<...\,0\,řešení\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,→Thaletova\, kružnice\, má\, 2\, průsečíky\, s \, kružnicí\, k\
\,\,\,\,\,\,\,∙=...\,1\,řešení\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,→Thaletova\, kružnice\, má\, vnitřní\, dotyk\, s\, kružnicí\, k\
\,\,\,\,\,\,\,∙>...\,0\,řešení\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,→Thaletova\, kružnice\, nemá\, žádný\, dotyk\,ani\, průsečík\, s\, kružnicí\, k\

Diskuze

Bod\, Q\, musí\, ležet\, uvnitř\, kružnice\, k!!!

Bod\, P\,\, musí\, ležet\, uvnitř\, kružnice\, k!!!

Dosazení do rovnice

r_k = 2.7 (slider from 0 to 10, step 0.1)
S = (2.611060815747595, 4.7415611314107124)
k = Circle(S, r_k)
P = (0.2953926567260664, 4.188565750151845)
Q = (4.753917918125726, 4.223127961480524)
A = Midpoint(P, Q)
Tk_{PQ} = Circle(A, Q)
C_2, C_1 = Intersect(Tk_{PQ}, k)
f = Ray(C_1, Q)
g = Ray(C_2, P)
h = Ray(C_2, Q)
i = Ray(C_1, P)
A_1 = Intersect(k, i, 2)
A_2 = Intersect(k, g, 2)
B_1 = Intersect(k, f, 2)
B_2 = Intersect(k, h, 2)
mnohoúhelník1, c_1, a_1, b_1 = Polygon(A_1, B_1, C_1)
a = false
b = false
e = false
j = false
k_1 = false
mnohoúhelník2, c_2, a_2, b_2 = Polygon(A_2, B_2, C_2)
l = false
c = false
d = false
m = false
n = false
o = false
p = true
q = false
r = Segment(P, Q)
s = Ray(P, Q)
B = Intersect(k, s, 1)
t = Segment(P, B)
f_1 = Ray(Q, P)
C = Intersect(k, f_1, 1)
g_1 = Segment(Q, C)
S_{PQ} = Midpoint(P, Q)
h_1 = Segment(S, S_{PQ})
i_1 = Segment(P, S_{PQ})
text5: "Dosazení\,\, do\,\, rovnice:\\" + (LaTeX[r_k]) + "-" + (LaTeX[h_1]) + "\,≟\," + (LaTeX[i_1]) + "\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\," + (LaTeX[r_k - h_1]) + "\,≟\," + (LaTeX[i_1]) + "\\
_{Upozornění:\, Velikosti\, jsou\, zaokrouhlené\, na\, 2\, desetinná\, místa!}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,_{Proto\, se\, Vám\, nejspíš\, nepodaří\, kružnice\,nakonfigurovat}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,_{ tak, \, aby\, měly\, pouze\, jeden\, vnitřní\, dotyk.}"
u = false