#include<cmath>
#include<algorithm>
#include<iostream>
#include<vector>
#include<string>
 
using namespace std;
 
double EPS = 1e-10;
 
double add(double a, double b){
  if(abs(a+b) < EPS * (abs(a)+abs(b)))return 0;
  return a+b;
}
 
struct point{
  double x, y;
  point(){}
  point(double x,double y) : x(x) , y(y){}
 
  point operator + (point p){
    return point(add(x,p.x), add(y,p.y));
  }
 
  point operator - (point p){
    return point(add(x,-p.x), add(y,-p.y));
  }
 
  point operator * (double d){
    return point(x*d,y*d);
  }
 
  point operator / (double d){
    return point(x/d,y/d);
  }
};
 
struct segment{ point a,b; };
 
struct circle{ point p; double r; };
 
double dot(point a, point b) { return (a.x * b.x + a.y * b.y); }
 
double cross(point a, point b) { return (a.x * b.y - a.y * b.x); }
 
int ccw(point p0, point p1, point p2){
  point a = p1 - p0;
  point b = p2 - p0;
  if(cross(a,b)>EPS)return +1;
  if(cross(a,b)<EPS)return -1;
  if(dot(a,b)<-EPS)return +2;
  if(a.x*a.x+a.y*a.y<b.x*b.x+b.y*b.y)return -2;
  return 0;
}
 
double vec_abs(point a){
  return sqrt(a.x*a.x+a.y*a.y);
}
 
double distance_ls_p(point a, point b, point c) {
  if ( dot(b-a, c-a) < EPS ) return vec_abs(c-a);
  if ( dot(a-b, c-b) < EPS ) return vec_abs(c-b);
  return abs(cross(b-a, c-a)) / vec_abs(b-a);
}
 
double dist(point a,point b){
  return sqrt(pow(a.x-b.x,2)+pow(a.y-b.y,2));
}
 
int crossCS(point a, point b, circle c){
  double res=distance_ls_p(a,b,c.p);
  double ac=dist(a,c.p);
  double bc=dist(b,c.p);
 
  if(res>c.r || (ac<c.r && bc<c.r))return 0;
  else if(c.r-res<EPS ||(ac<c.r && bc>=c.r)||(ac>=c.r && bc<c.r))return 1;
  else return 2;
}
 
 bool cmp_x(const point& p, const point& q){
  if(p.x != q.x)return p.x<q.x;
  return p.y < q.y;
}

vector<point>convex_hull(point* ps, int n){
  sort(ps,ps+n,cmp_x);
  int k=0;
  vector<point>qs(n*2);
 
  for(int i=0;i<n;i++){
    while(k>1&&cross(qs[k-1]-qs[k-2],ps[i]-qs[k-1])<0)k--;
    qs[k++]=ps[i];
  }
 
  for(int i=n-2,t=k;i>=0;i--){
    while(k>t&&cross(qs[k-1]-qs[k-2],ps[i]-qs[k-1])<0)k--;
    qs[k++]=ps[i];
  }
  qs.resize(k-1);
  return qs;
}

int point_contain(point* ps, point p, int n){
  int cnt=ccw(ps[0],ps[1],p);
  ps[n++]=ps[0]; 

  for(int i=0;i<n-1;i++)
    if(cnt!=ccw(ps[i],ps[i+1],p))return 0;
   
  return 1;
}
 
int crossCP(point* ps, circle C, int sz){
 
  double ans=0;
 
  for(int i=0;i<sz;i++){
    double tmp=dist(ps[i],C.p);
    if(tmp>ans)ans=tmp;
  }
 
  if(C.r>=ans)return 2;
 
  vector<point>t=convex_hull(ps,sz);

  int tsz=t.size();
  int res1=point_contain(ps,C.p,tsz);
 
  double res2=100000000;
   t[t.size()]=t[0];
   tsz++;
  for(int i=0;i<tsz-1;i++)
    res2=min(res2,distance_ls_p(t[i],t[i+1],C.p));
 
  if(res1 && C.r<=res2)return 1;
  else if(!res1 && C.r<res2)return 4;
  else return 3;
}
 
int main(void){
  point p[3];
  vector<segment> t;
  circle C;
  string ans="zabcd";
 
  while(true){
    for(int i=0;i<3;i++){
      cin >> p[i].x >> p[i].y;
      if(p[i].x==0 && p[i].y==0)return 0;
    }
    cin >> C.p.x >> C.p.y >> C.r;
 
    int res=crossCP(p,C,3);
    cout << ans[res] << endl;
  }
  return 0;
}