A = (-4.15677660913365, -4.17643807607806, 0)
B = (4.32, -4.5, 0)
C = Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]])
a, D, FlächeABC, FlächeACD, FlächeABD, FlächeBCD, KanteAC, KanteAB, KanteBC, KanteAD, KanteCD, KanteBD = Tetrahedron(A, B, C)
f = LineBisector(KanteAB, xOyPlane)
g = LineBisector(KanteBC, xOyPlane)
U_1 = Intersect(g, f)
F = Midpoint(C, A)
G = Midpoint(A, D)
h = Segment(C, G)
i = Segment(D, F)
U_2 = Intersect(h, i)
j = OrthogonalLine(U_1, xOyPlane)
k = OrthogonalLine(U_2, FlächeACD)
M = Intersect(k, j)
b = Sphere(M, B)
p = Plane(D, M, B)
d1, b_1, m, u_1 = Polygon(M, U_1, B)

Tool: MiPu
Input: A, B, C
Output: E

a, D, FlächeABC, FlächeACD, FlächeABD, FlächeBCD, KanteAC, KanteAB, KanteBC, KanteAD, KanteCD, KanteBD = Tetrahedron(A, B, C)
f = LineBisector(KanteAB, xOyPlane)
g = LineBisector(KanteBC, xOyPlane)
E = Intersect(g, f)