Are the squares axis-aligned (as in the sample) ?
I understand the circles are not symmetric, how deformed can they be? can they be tilted ellipses?
Why a problem with such unclear requirements?

Some new tests were added. 18 authors lost AC verdict.

Q1. A square can be rotated to some angle (for example, 30 degrees)?

Q2. If answer to Q1 NO then:
   what wrong in my program:
-----------------------------------------------------------
program Task;

{$APPTYPE CONSOLE}

{ Task #1378 }

var Matrix: array [1..1000,1..1000] of boolean;
    W, H:   integer;
    i, j:   integer;
    maxX,
    minX,
    maxY,
    minY:   integer;
    S, p:   longint;
    strin:  string;

begin
     { Some code :) } <-- it was deleted by me :)
end.

Edited by author 15.05.2006 21:40

Edited by author 17.05.2006 20:12

My program have WA1,but it's give me a correct answer for a test from task.

#include <iostream.h>
#include <stdio.h>
int main(){
long h,w,j,i=0;
double k,s=0,p=0;
long ar[110][110];
char c=0;
cin >>w >>h;
while (i<w*h && c!=EOF) {
if (c=='0' || c=='1') {ar[i/w+1][i%w+1]=c-'0';i++;}
c=getchar();
}
for (i=0;i<=h;i++){ar[i][0]=0;ar[i][w+1]=0;}
for (i=0;i<=w;i++){ar[0][i]=0;ar[h+1][i]=0;}
for (i=1;i<=h;i++)
    for (j=1;j<=w;j++) {
         if (ar[i][j]==1) s++; else continue;
         if (ar[i-1][j]==0 || ar[i+1][j]==0 || ar[i][j-1]==0 || ar[i][j+1]==0) p++;
         }
p=p+3;
k=p*p/s;
if (k<13) printf("circle");
      else if (k<18) printf("square");
      else printf("triangle");

return 0;
}

Maybe I have some problem with input?
P.S
Sorry,for my bad english.

I got AC, but I think there's something wrong with thest 6. Apparently it's a triangle, but in the bounding box of the triangle there are 4 (!) separate 0-areas (all of at least 10 pixels). This should not be possible beacuse a triangle can separate at most 3 0-areas inside the bounding box.

admin why circle(in test2) not simmytrican into centrel????
You sure when test2 correct?
Please answer somthink(correct or fixed).