Sestrojte\ trojúhelník\ ABC,\ pokud\ známe:\ \
\,\,\,\,\,\,\,\,\,\,\,\alpha,\ t_a,\ r\,(poloměr\ kružnice\ opsané)

2α

ΔA_1BC

ΔA_2BC

l; l(T_a, t_a)

k ∩ l = {A_1, A_2}

T_a; T_a ∈ |BC|; |BT_a| = |T_aC|

|BC|; k ∩ →OX' = B, k ∩ →OY' = C

k; k(O, r)

Orientovaný úhel X'OY', |∢X'OY'| = 2α

1

2

3

4

5

6

7

Postup

0°<α<180°\ 
α+β+γ=180°\

r

t_a

\underline{Počet\  řešení:} \
\ \ \   ∙\ 2\ řešení\ ......\  α<\frac{π}{2}\ ∧\ |T_aO|+r>t_a>r-|T_aO|\
\ \ \   ∙\ 1\ řešení\ ......\  α<\frac{π}{2}\ ∧\ |T_aO|+r=t_a=r-|T_aO|\
\ \ \   ∙\ 0\ řešení\ ......\  α<\frac{π}{2}\ ∧\ |T_aO|+r<t_a<r-|T_aO|\
\ \ \   ∙\ ∞\ řešení\ ....\  α=\frac{π}{2}\ ∧\ t_a=r

Počet řešení

Zadání = true
α = 1.9547687622336491 rad (slider from 0 to 180°, step °)
X' = (5.24, 4.22)
O = (6.3777, 3.56822)
Y' = Rotate(X', (2 * α), O)
β = Angle(X', O, Y')
f = Ray(O, X')
g = Ray(O, Y')
r = 4 (slider from 0.1 to 10, step 0.1)
k = Circle(O, r)
B = Intersect(k, f, 1)
C = Intersect(k, g, 1)
h = Segment(B, C)
T_a = Midpoint(B, C)
t_a = 3.4 (slider from 0.1 to 10, step 0.1)
l = Circle(T_a, t_a)
A_2, A_1 = Intersect(l, k)
mnohoúhelník1, c, a_1, b = Polygon(A_1, B, C)
mnohoúhelník2, c_1, a_2, b_1 = Polygon(A_2, B, C)
d = false
e = false
i = false
j = false
m = false
n = false
o = false
a = false
p = false
A = Point(k)
q = Segment(O, A)
D = Point(l)
s = Segment(T_a, D)
t = Segment(T_a, O)
u = false