BeginPackage["Arc`"]

Arc::usage = "\n
   Arc[a,b,c] draws the arc from a to b going through c.\n
   The arguments should be pairs of numbers.\n"

Begin["`private`"]

Arc[a:{_,_},b:{_,_},c:{_,_}] :=
  Block[{sol=NullSpace[{Append[a-b,(a.a-b.b)/2],Append[c-b,(c.c-b.b)/2]}]},
    If[Length[sol]>1, Indeterminate, (* two or more points coincide *)
      If[sol[[1,-1]]==0, foo[a,b,c], (* points are aligned *)
        Block[{center=Drop[sol[[1]],-1]/-sol[[1,-1]],angles},(* generic case *)
          angles=fixangles[N[ArcTan@@(#-center)]& /@ {a,b,c}];
          If[angles[[2]]-angles[[1]]<.000001,foo[a,b,c],
            Circle[center,Sqrt[len2[center-a]],angles]]]]]]

len2[x_] := x.x
between[a_,b_,c_] := OrderedQ[{a,b,c}] || OrderedQ[{c,b,a}]

foo[a_,b_,c_] := If[between[a,b,c], Line[{a,c}], LineComplement[{a,c}]]

fixangles[{a_,b_,c_}] :=
  If[between[a,b,c], Sort[{a,c}], Sort[{a,c+2Sign[a-c]N[Pi]}]]

End[]
EndPackage[]