Morley mit Winkelsubtraktion

source  =  
        DirectoryName[
          ToFileName["FileName" /. 
              NotebookInformation[EvaluationNotebook[]]]];
SetDirectory[source];
Needs["GeoBeweiser`"]

clearndg[];
Clear[u1, u2, u3, x1, x2, x3, x4, x5, x6, y];

vars := {x1, x2, x3, x4, x5, x6, y};
parameters := {u1, u2, u3};

Unprotect[C, D, E];
A = point[0, 0]; B = point[u1, 0];
C = point[u2, u3];
D = point[x5, x6]; E = point[x1, x2];
F = point[x3, x4];
X = point[x7, x8];

AddGleichung[
        dreiteilung[p3angle[B, A, C], p3angle[B, A, D]]];

AddGleichung[
        dreiteilung[p3angle[C, B, A], p3angle[C, B, E]]];

AddGleichung[
        dreiteilung[p3angle[A, C, B], p3angle[A, C, F]]];

Bad = sympoint[B, ppline[A, D]]

Acf = sympoint[A, ppline[C, F]]

Cbe = sympoint[C, ppline[B, E]]

AddGleichung[online[E, ppline[Acf, C]]]

AddGleichung[online[F, ppline[Bad, A]]]

AddGleichung[online[D, ppline[Cbe, B]]]

polys = Map[Numerator[Together[#]] &, Gleichungen]

con1 = 
      sqrdist[D, E] - sqrdist[E, F]

con2 = sqrdist[D, E] - sqrdist[D, F]

IdealMember[con1, polys, vars] // Timing

IdealMember[con2, polys, vars] // Timing