#include <iostream>
#include <string>
#include <cstdlib>
#include <cmath>
#include <fstream>

using namespace std;

struct Point{
  int x;
  int y;
};

struct Delta{
  Point p[3];
};

struct Circle{
  Point p;
  int radius;
};

double distance(Point p1, Point p2){
  return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}

double dist_line(Point pl1, Point pl2, Point p){
  int a = pl1.x - pl2.x;
  int b = pl2.y - pl1.y;
  int c = pl1.y * pl2.x - pl1.x * pl2.y;
  double ans = b * p.x + a * p.y + c;
  ans = (ans >= 0) ? ans : -ans;
  return ans / sqrt(a*a + b*b);
}
int main(void){
  string str;
  ifstream ifs("../input.txt");
  if (ifs.fail()) {
	  cerr << "cannot find the file" << endl;
	  return 1;
  }
  while(1){
    Circle *c = (Circle *) malloc(sizeof(Circle));
	Delta *d = (Delta *) malloc(sizeof(Delta));
	for (int i = 0; i < 5; i++) {
		getline(ifs, str);

      if(str == "0 0") break;
	  
      int j;
      for(j = 0; j <(int) str.size(); j++){
	      if(str[j] == ' '){			
			str[j] = '\0';
			break;
        }
      }
      switch(i){
        case 0:
        case 1:
        case 2:
        d->p[i].x = atoi(str.c_str());
        d->p[i].y = atoi(&str[j+1]);
        break;
        case 3:
        c->p.x = atoi(str.c_str());
        c->p.y = atoi(&str[j+1]);
        break;
        case 4:
        c->radius = atoi(str.c_str());
        break;
      }
	  
    }
    if(str == "0 0") break;
	

    if(distance(d->p[0], c->p) <= c->radius&& distance(d->p[1], c->p) <= c->radius&& distance(d->p[2], c->p) <= c->radius){
      cout << 'b' << endl;
    }
    else if(dist_line(d->p[0], d->p[1], c->p) >= c->radius&& dist_line(d->p[0], d->p[2], c->p) >= c->radius&& dist_line(d->p[1], d->p[2], c->p) >= c->radius){
		if (dist_line(d->p[0], d->p[1], d->p[2]) <= distance(d->p[0], c->p) && dist_line(d->p[1], d->p[2], d->p[0]) <= distance(d->p[1], c->p) && dist_line(d->p[2], d->p[0], d->p[1]) <= distance(d->p[2], c->p))
			cout << 'd' << endl;
		else
			cout << 'a' << endl;
    }
    else if(dist_line(d->p[0], d->p[1], c->p) <= c->radius|| dist_line(d->p[0], d->p[2], c->p) <= c->radius|| dist_line(d->p[1], d->p[2], c->p) <= c->radius){
      cout << 'c' << endl;
    }
    else{

    }
	
  }
  return 0;
}