Neoznačený

Equilateral triangle 

Let A, B points  in c
Circle center A  through B
Circle center B  through A
E intersection of circles

help

O = (0, 0)
R = (1, 0)
c = Circle((0, 0), 1)
A = (-0.7675575261752019, -0.16354629150241082)
B = (0.44365696037233276, -0.579109420778137)
d = segH(c, A, B)
e = rettaH(O, R, A, B)
C = Point(c)
A' = Mirror(A, c)
a = Ray(O, A)
b, i = Tangent(B, d)
D = Intersect(b, a)
g = Ray(O, B)
h, j = Tangent(A, d)
F = Intersect(h, g)
f = Circle(D, B)
k = Circle(F, A)
E, G = Intersect(f, k)
p = segH(c, B, E)
q = segH(c, E, A)
A'_1 = Mirror(A, c)
B' = Mirror(B, c)
E' = Mirror(E, c)
circ_{AE} = Circle(A'_1, A, E)
circ_{EB} = Circle(E, B, B')
circ_{AB} = Circle(A, B, B')
O_{AB} = Center(circ_{AB})
O_{AE} = Center(circ_{AE})
O_{EB} = Center(circ_{EB})
reg_{AB}(x, y) = (x - x(O_{AB}))^(2) + (y - y(O_{AB}))^(2) > Distance[O_{AB}, A]^(2)
reg_{AE}(x, y) = (x - x(O_{AE}))^(2) + (y - y(O_{AE}))^(2) > Distance[O_{AE}, A]^(2)
reg_{EB}(x, y) = (x - x(O_{EB}))^(2) + (y - y(O_{EB}))^(2) > Distance[O_{EB}, E]^(2)
triangolo(x, y) = reg_{AB}(x, y) ∧ reg_{AE}(x, y) ∧ reg_{EB}(x, y)
help = true
H = (-0.6509971362564018, 0.5104768328106571)
I = (-0.2506375361005221, 0.5864944784098753)
J = (-0.3266551816997397, 0.42432350113154316)
K = (-0.5496402754574449, 0.22160977953362795)
L = (-0.5901830197770276, 0.11518507569472244)
M = Point(q)
N = Point(p)
l = distH(K, L, M, N)

Tool: rettaH
centro O, punto R, punti A e B
Input: O, R, A, B
Output: e

c = Circle(O, R)
A' = Mirror(A, c)
d = Circle(A', A, B)
C, D = Intersect(c, d)
e = CircumcircleArc(D, A, C)

Tool: circleH
circleH[ <Point>, <Point>, <Point>, <Point> ]
Input: O, R, A, B
Output: f

c = Circle(O, R)
A' = Mirror(A, c)
d = Circle(A', A, B)
C, D = Intersect(c, d)
e = CircumcircleArc(D, A, C)
a = Line(O, A)
b = Tangent(B, e)
E = Intersect(b, a)
f = Circle(E, B)

Tool: ortoH
centro O, punto R, retta A,B, punto H
Input: O, R, A, B, H
Output: q

c = Circle(O, R)
g = rettaH(O, R, A, B)
h = circleH(O, R, H, A)
F, J = Intersect(h, g)
k = circleH(O, R, A, F)
p = circleH(O, R, F, A)
K, L = Intersect(p, k)
q = rettaH(O, R, L, H)

Tool: reflectH
centro O, punto R, retta g, punto H
Input: O, R, g, H
Output: H'

c = Circle(O, R)
A = PointIn(c)
B = PointIn(c)
H' = Mirror(H, g)

Tool: orto2H
centro O, punto R, retta r, punto P in r
Input: O, R, r, P
Output: t

c = Circle(O, R)
P' = Mirror(P, c)
i = LineBisector(P', P)
j = Tangent(P, r)
Q = Intersect(i, j)
s = Circle(Q, P')
S, T = Intersect(s, c)
t = CircumcircleArc(T, P, S)

Tool: distH
centro O, punto R, punti H e K
Input: O, R, H, K
Output: dH

δ: (2 * Distance[H, K]^(2) / (1 - Distance[H, O]^(2)) / (1 - Distance[K, O]^(2)))
dH: acosh(1 + δ)

Tool: segH
segH[ <Circle>, <Point>, <Point> ]
Input: c, A, B
Output: seg_{AB}

O = Center(c)
B' = Mirror(B, c)
d = Circle(A, B, B')
a = Segment(A, B)
b = OrthogonalLine(O, a)
seg_{AB} = If(Length[CircumcircleArc[A, Intersect[d, b, 1], B]] ≤ Length[CircumcircleArc[A, Intersect[d, b, 2], B]], CircumcircleArc[A, Intersect[d, b, 1], B], CircumcircleArc[A, Intersect[d, b, 2], B])