[math-fun] 2nd intersection

I hope Henry or someone is collecting our various complex number geometricks e.g., PolygonArea[L_List] := Total[MapThread[Im[#1\[Conjugate]*#2] &, {L, RotateLeft[L]}]]/2 line segment intersect Interseg[z1_, z2_, z3_, z4_] := Block[{z12 = z1 - z2, z34 = z3 - z4}, (z34*Im[z2*z1\[Conjugate]] + z12*Im[z3*z4\[Conjugate]])/Im[z34*z12\[Conjugate]]] incenter, circumcenter, inradius, ... . For the Clifford circle theorems I needed second intersection: Given centers of circles though the origin z1, z2, secondintersection[z1_, z2_] := (Conjugate[z1] z2 - Conjugate[z2] z1)/Conjugate[z1 - z2] Is this obvious to anybody? I had to derive it with 8th grade analytic geometry. --rwg