A = (-2.352300693130755, 0.4999505374807373)
B = (-0.5267780126345885, 1.0935253967831717)
C = (-0.851564256403845, -0.9559877966573095)
poly1, c, a, b = Polygon(A, B, C)
α = 2.4000000000000004 (slider from -5 to 5, step 0.1)
β = 1.1000000000000005 (slider from -5 to 5, step 0.1)
γ = 1 (slider from -5 to 5, step 0.1)
G = Barycentrede3points(A, α, B, β, C, γ)
H: A + β / (α + β) Vector[A, B]
d = Segment(H, C)

Tool: Barycentre de 3 points (command Barycentrede3points)
Input: A, α, B, β, C, γ
Output: G

v: β / (α + β + γ) Vector[A, B] + γ / (α + β + γ) Vector[A, C]
G = Translate(A, v)