#include <iostream>
#include <complex>
#include <cmath>
using namespace std;

#define rep(i, n) for(int i = 0; i < n; i++)
typedef complex<double> xy_t;
typedef pair<xy_t, xy_t> line;
const double EPS = 1e-10;

double cross(const xy_t &a, const xy_t &b){
  return imag(conj(a) * b);
}

double dot(const xy_t &a, const xy_t &b){
  return real(conj(a) * b);
}

xy_t projection(const line &l, const xy_t &p){
  double t = dot(l.second - l.first, p - l.first) / norm(l.second - l.first);
  return l.first + t * (l.second - l.first);
}

bool intersectSP(const line &l, const xy_t &p){
  if(abs(p - l.first) + abs(p - l.second) < abs(l.first - l.second) + EPS) return true;
  else return false;
}

double distanceSP(const line &l, const xy_t &p){
  xy_t r = projection(l, p);
  if(intersectSP(l, r)) return abs(r - p);
  else return min(abs(l.first - p), abs(l.second - p));
}

int ccw(xy_t a, xy_t b, xy_t c){
  b -= a, c -= a;
  if(cross(b, c) > 0) return 1;
  if(cross(b, c) < 0) return -1;
  if(dot(b, c) < 0) return 2;
  if(norm(b) < norm(c)) return -2;
  return 0;
}
 
xy_t p[3];
line l[3];
xy_t c;
double r;


int main(){
  int x, y;
  int c1, c2;
  while(cin >> x>> y && (x || y)){
    p[0] = xy_t(x, y);
    for(int i = 1; i < 3; i++) {
      cin >> x >> y;
      p[i] = xy_t(x, y);
    }
    cin >> x >> y;
    cin >> r;
    c = xy_t(x, y);
    
    rep(i, 3) l[i] = line(p[i], p[(i+1)%3]);
    c1 = 0, c2 = 0;
    int cnt = 0;

    rep(i, 3){
      int d = ccw(p[i], p[(i+1)%3], c);
      if(d >= 0) c1++;
      if(d <= 0) c2++;
    }
    bool circle_in[3];
    rep(i, 3){
      if(distanceSP(l[i], c) > r - EPS){
	circle_in[i] = true;
      }else{
	circle_in[i] = false;
	cnt++;
      }
    }
    
    bool t_in[3];
    rep(i, 3){
      if(abs(c - p[i]) < r + EPS){
	t_in[i] = true;
	cnt++;
      }else{
	t_in[i] = false;
      }
    }
    if(circle_in[0] && circle_in[1] && circle_in[2] && max(c1, c2) == 3){
      cout << 'a' << endl;
    }else if(t_in[0] && t_in[1] && t_in[2]) {
      cout << 'b' << endl;
    }else if(cnt > 0){
      cout << 'c' << endl;
    }else{
      cout << 'd' << endl;
    }
  }
  return 0;
}