Как нарисовать серединные перпендикуляры к сторонам треугольника на плоскости Лобачевского в модели верхней полуплоскости?

Manipulate[
 h[z_, {a_, b_, c_, d_}] := 
  If[ad - bc > 0, (az + b)/(cz + d), (-az - b)/(cz + d)];
 linepl[z1_, z2_, t_] := 
  Module[{p1, p2, med, hp1, hp2, centr, r, hp, s, tt},
   p1 = {Re[z1], Im[z1]};
   p2 = {Re[z2], Im[z2]};
   med = (p1 + p2)/2;
   intpt = Solve[med[[2]] + s (p1[[1]] - p2[[1]]) == 0, s, Reals];
   s0 = If[Length[intpt] == 1, s /. intpt[[1]], E^\[Pi]];
   cent = {med[[1]] + s0 (p2[[2]] - p1[[2]]), 0};
   r = Sqrt[(p2 - cent).(p2 - cent)];
   hp1 = (z1 - (cent[[1]] + r))/(z1 - (cent[[1]] - r)) // FullSimplify;
   hp2 = (z2 - (cent[[1]] + r))/(z2 - (cent[[1]] - r)) // FullSimplify;
   hp[tt_] := (-(hp1 + tt (hp2 - hp1)) (cent[[1]] - r) + (cent[[1]] + 
       r))/(1 - (hp1 + tt (hp2 - hp1)));
   If[Length[intpt] == 1, {Re[hp[t]], Im[hp[t]]}, p1 + t (p2 - p1)]
   ];
 PlPoly[p_, Clr_] := Module[{},
   Show[{
     Table[ParametricPlot[With[{z = linepl[Complex[Sequence @@ p[[i]]],
           Complex[Sequence @@ p[[If[i == Length[p], 1, i + 1]]]], t]},
        {Re[z], Im[z]}], {t, 0, 1}, PlotStyle -> Directive[Clr]],
      {i, If[Length[p] == 2, 1, Length[p]]}]
     }, ImageSize -> {300, 300}, PlotRange -> {{-5, 5}, {0, 5}}]
   ];
 gtable[p_, {a_, b_, c_, d_}] := 
  Table[{Re[h[Complex[p[[i]][[1]], p[[i]][[2]]], {a, b, c, d}]],
    Im[h[Complex[p[[i]][[1]], p[[i]][[2]]], {a, b, c, d}]]}, {i, 1, 
    Length[p]}];
 Row[{PlPoly[p, Red], PlPoly[gtable[p, {a, b, c, d}], Blue]}],
 {{a, 1}, -2, 2, 0.1}, {{b, 0}, -1, 1, 0.1}, {{c, 0}, -1, 1, 
  0.1}, {{d, 1}, -2, 2, 0.1}, {{p, {{0, 1}, {2, 1}, {1, 3}}}, Locator}]