1814.cpp

//Written by RR

{$MODE OBJFPC}

uses math;
const
  FINP          =       '';
  FOUT          =       '';
  MAXN          =       100111;
  eps           =       1e-9;

type
  point         =       record x,y:double; end;
  circle        =       record x,y,r:double; end;

var
  f1,f2         :       text;
  test,n        :       longint;
  a             :       array[1..MAXN] of point;
  res           :       circle;

procedure openF;
    begin
      assign(f1,FINP); reset(f1);
      assign(f2,FOUT); rewrite(f2);
    end;

procedure closeF;
    begin
      close(f1);
      close(f2);
    end;

procedure inp;
    var
      i:longint;
    begin
      read(f1,n);
      for i:=1 to n do
        with a[i] do
          read(f1,x,y);
    end;

procedure update2(a,b:point);
    begin
      res.x:=(a.x+b.x)/2;
      res.y:=(a.y+b.y)/2;
      res.r:=sqr(a.x-res.x) + sqr(a.y-res.y);
    end;

procedure update3(a,b,c:point);
    var
      s,u,v:double;
    begin
      u:=(c.y-b.y)/2-(c.x-b.x)*(a.x-b.x)/2/(b.y-a.y);
      v:=(c.y-a.y)*(a.x-b.x)/(b.y-a.y)-(a.x-c.x);
      s:=u/v;
      res.x:=(a.x+c.x)/2+s*(c.y-a.y);
      res.y:=(a.y+c.y)/2+s*(a.x-c.x);
      res.r:=sqr(a.x-res.x)+sqr(a.y-res.y);
    end;

function isInside(a:point):boolean;
    begin
      exit( sqr(a.x-res.x) + sqr(a.y-res.y) < res.r+eps );
    end;

procedure solve;
    var
      i,j,k:longint;
    begin
      update2(a[1],a[2]);
      for i:=3 to n do
        if not isInside(a[i]) then
          begin
            update2(a[1],a[i]);
            for j:=1 to i-1 do
              if not isInside(a[j]) then
                begin
                  update2(a[i],a[j]);
                  for k:=1 to j-1 do
                    if not isInside(a[k]) then
                      update3(a[i],a[j],a[k]);
                end;
          end;
      writeln(f2,sqrt(res.r):0:2);
      writeln(f2,res.x:0:2,' ',res.y:0:2);
    end;

begin
  openF;
  read(f1,test);
  for test:=1 to test do
    begin
      inp;
      solve;
    end;
  closeF;
end.