Pythagoras

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

clearndg[];
Clear[u1, u2, u3, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, 
        x13, x14, y];

vars := {y};
parameters := {u1, u2, u3};

Unprotect[
        C];

    A = point[0, 0];

    B = point[u1, 0];

    C = point[u2, u3];

a = 
      ppline[B, C]

b = ppline[A, C]

c = ppline[A, B]

AddGleichung[isorthogonal[a, b]]

(* polynomials *)
polys=Map[Numerator[Together[#]] &, Gleichungen]

con = sqrdist[A, B] - (sqrdist[B, C] + sqrdist[A, C])

IdealMember[con, polys, vars] // Timing