Select your Soddy center 175 or 176

            Drag A
Then change A2 value

S: Soddy\ center\ selected\ in\ cell\ A2\
i_a, i_b, i_c: incircles\ of\ SBC,\ SCA,\ SAB\ (resp) 

Angle β=

Angle γ=

Angle α=

tg(α / 2) + tg(β / 2) + tg(γ / 2)

Are incircles mutually tangent?

B = (-75.55512630978481, -30.885909333438164)
C: (13.792709524240522, y(B))
a = Segment(B, C)
a_1 = Line(B, C)
D = (-126.56056782144297, 69.79149809480192)
d = Line(D, a_1)
A = Point(d)
c = Segment(A, B)
b = Segment(C, A)
Delta: sqrt(((((a + b + c) * ((-a) + b + c)) * (a - b + c)) * (a + b - c))) / 4
A2: 176
S = TriangleCenter(A, B, C, If[A2 ≟ 175 ∨ A2 ≟ 176, A2, 0])
a' = Segment(S, A)
b' = Segment(S, B)
c' = Segment(S, C)
i_a = Incircle(S, B, C)
i_b = Incircle(S, C, A)
i_c = Incircle(S, A, B)
B' = Proyeccion(B, d)
C' = Proyeccion(C, d)
h = Line(B, B')
i = Line(C, C')
β = Angle(C, B, A)
γ = Angle(A, C, B)
I_a = Center(i_a)
I_b = Center(i_b)
I_c = Center(i_c)
α = Angle(B, A, C)
A5: α
A14: tan(α / 2) + tan(β / 2) + tan(γ / 2)
A17: b' + c' + (If[A2 ≟ 175, 1, -1] * a)
A18: c' + a' + (If[A2 ≟ 175, 1, -1] * b)
A19: a' + b' + (If[A2 ≟ 175, 1, -1] * c)
A11: γ
A8: β
A20: A17 ≟ A18 ∧ A18 ≟ A19
A23: circSonTangentes[i_b, i_c] ∧ circSonTangentes[i_c, i_a] ∧ circSonTangentes[i_a, i_b]
A16 = If(A2 ≟ 175, "Is S isoperimetric?", "Is S Equal detour?")

Tool: Proyeccion
Punto, recta
Input: A, a
Output: D

b = OrthogonalLine(A, a)
D = Intersect(a, b)

Tool: EjeRadical
c1, c2
Input: c, d
Output: a

E = Center(c)
F = Center(d)
E' = Mirror(E, d)
F' = Mirror(F, c)
a = LineBisector(F', E')

Tool: TrazaRadical
c1, c2
Input: c, d
Output: G

E = Center(c)
F = Center(d)
E' = Mirror(E, d)
F' = Mirror(F, c)
a = Line(E, F)
b = LineBisector(F', E')
G = Intersect(a, b)

Tool: CentroRadical
c1,c2,c3
Input: c, d, e
Output: Q

E = Center(c)
F = Center(d)
J = Center(e)
a = EjeRadical(c, d)
b = EjeRadical(e, c)
f = EjeRadical(e, d)
Q = If(AreConcurrent[a, b, f], Intersect[a, b], Trilinear[E, F, J, 0, 0, 0])

Tool: CircRadical
c1, c2, c3
Input: c, d, e
Output: g

E = Center(c)
G = CentroRadical(c, d, e)
K = Midpoint(E, G)
f = Circle(K, E)
L, M = Intersect(f, c)
g = Circle(G, M)

Tool: Exsimilcenter
c1,c2
Input: c, d
Output: J

E = Center(c)
F = Center(d)
E' = Rotate(E, 45°, E)
F' = Rotate(F, 45°, E)
a' = Ray(E', F')
E'_1 = Mirror(E, F)
F'_1 = Rotate(F, 45°, F)
G = Rotate(E'_1, 45°, F)
b' = Ray(F'_1, G)
H = Intersect(c, a')
I = Intersect(d, b')
e = Line(E, F)
f = Line(H, I)
J = Intersect(e, f)

Tool: Insimilcenter
c1, c2
Input: c, d
Output: L

E = Center(c)
F = Center(d)
E' = Rotate(E, 45°, E)
F' = Rotate(F, 45°, E)
a' = Ray(E', F')
E'_1 = Mirror(E, F)
G = Rotate(E'_1, 45°, F)
H = Intersect(c, a')
e = Line(E, F)
g = Ray(G, F)
K = Intersect(d, g, 2)
h = Line(H, K)
L = Intersect(e, h)

Tool: CircPolar
circ, point
Input: c, G
Output: b

b = Polar(G, c)

Tool: CircPolo
Circ, recta
Input: c, a
Output: I'

E = Center(c)
b = OrthogonalLine(E, a)
I = Intersect(a, b)
I' = Mirror(I, c)

Tool: Excircle
A,B,C
Input: J, K, L
Output: e

Q = Trilinear(J, K, L, -1, 1, 1)
Q' = Proyeccion(Q, Line[K, L])
e = Circle(Q, Q')

Tool: Incircle
A,B,C
Input: J, K, L
Output: e

Q = TriangleCenter(J, K, L, 1)
Q' = Proyeccion(Q, Line[K, L])
e = Circle(Q, Q')

Tool: uvw (command uvw1)
A,B,C,P
Input: A, B, C, P
Output: lista3

A' = Intersect(Line[A, P], Line[B, C])
B' = Intersect(Line[B, P], Line[C, A])
C' = Intersect(Line[C, P], Line[A, B])
u: (If[Min[x(A), x(P)] ≤ x(A') ∧ x(A') ≤ Max[x(A), x(P)] ∧ Min[y(A), y(P)] ≤ y(A') ∧ y(A') ≤ Max[y(A), y(P)], -1, 1] * Distance[P, Line[B, C]])
v: (If[Min[x(B), x(P)] ≤ x(B') ∧ x(B') ≤ Max[x(B), x(P)] ∧ Min[y(B), y(P)] ≤ y(B') ∧ y(B') ≤ Max[y(B), y(P)], -1, 1] * Distance[P, Line[C, A]])
w: (If[Min[x(C), x(P)] ≤ x(C') ∧ x(C') ≤ Max[x(C), x(P)] ∧ Min[y(C), y(P)] ≤ y(C') ∧ y(C') ≤ Max[y(C), y(P)], -1, 1] * Distance[P, Line[A, B]])
lista3: {u, v, w}

Tool: BuscaCentro
BuscaCentro[ <Punto>, <Punto>, <Punto>, <Punto> ]
Input: A, B, C, D
Output: z

z = IndexOf(D, Sequence[TriangleCenter[A, B, C, k], k, 1, 3053])

Tool: xyz
A,B,C,P
Input: A, B, C, Q
Output: XYZ

B: (0, 0)
a = Segment(B, C)
b = Segment(C, A)
c = Segment(A, B)
a' = Line(B, C)
b' = Line(A, C)
c' = Line(A, B)
A' = Intersect(Line[A, Q], a')
B' = Intersect(Line[B, Q], b')
C' = Intersect(Line[C, Q], c')
u_a: (Distance[Q, a'] * sgn(Distance[A, A'] - Distance[A, Q]))
u_b: (Distance[Q, b'] * sgn(Distance[B, B'] - Distance[B, Q]))
u_c: (Distance[Q, c'] * sgn(Distance[C, C'] - Distance[C, Q]))
U: {u_a, u_b, u_c}
X_1: (U * {a, b, c})
sm = Sum(X_1)
XYZ: X_1 / If[sm ≟ 0, 1, sm]

Tool: CircConcurren
c1,c2,c3
Input: c, d, e
Output: A2

I = CentroRadical(e, d, c)
A2: Distance[I, c] ≟ 0 ∧ Distance[I, d] ≟ 0 ∧ Distance[I, e] ≟ 0

Tool: circSonOrtogonales
c1, c2
Input: c, d
Output: e

E, F = Intersect(c, d)
a = Tangent(E, c)
b = Tangent(E, d)
e = ArePerpendicular(a, b)

Tool: circSonTangentes
c1,c2
Input: c_1, c_2
Output: a

O_1 = Center(c_1)
O_2 = Center(c_2)
d = Distance(O_1, O_2)
r_1 = Radius(c_1)
r_2 = Radius(c_2)
a: (d > 0 ∨ r_1 ≠ r_2) ∧ (d ≟ r_1 + r_2 ∨ d ≟ abs(r_1 - r_2))