#include<algorithm>
#include<iostream>
#include<string>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
using namespace std;
void f(double& v,double& w,double& x,double& y,int& n,int bx,int by,int ex,int ey,int cx,int cy,int cr){
  double vx,vy,px,py,ds;
  ds=sqrt((ex-bx)*(ex-bx)+(ey-by)*(ey-by));
  vx=(ex-bx)/ds;
  vy=(ey-by)/ds;
  ds=((ey-by)*cx+(bx-ex)*cy+(by-ey)*bx+(ex-bx)*by)/((ey-by)*vy-(bx-ex)*vx);
  px=cx-vy*ds;
  py=cy+vx*ds;
  if(0){
  }else if(cr>ds){
    n=2;
    ds=sqrt(cr*cr-ds*ds);
    v=px+vx*ds;
    w=py+vy*ds;
    x=px-vx*ds;
    y=py-vy*ds;
  }else if(cr<ds){
    n=0;
  }else{
    n=1;
    v=px;
    w=py;
  }
  return;
}
int g(int bx,int by,int ex,int ey,int cx,int cy,int cr){
  int n;
  double v,w,x,y;
  f(v,w,x,y,n,bx,by,ex,ey,cx,cy,cr);
  if(0){
  }else if(n==0){
    return 0;
  }else if(n==1){
    if(bx==ex)
      return (min(by,ey)<w&&w<max(by,ey))*2;
    else
      return (min(bx,ex)<v&&v<max(bx,ex))*2;
  }else{
    if(bx==ex)
      return min(by,ey)<min(w,y)&&max(w,y)<max(by,ey);
    else
      return min(bx,ex)<min(v,x)&&min(v,x)<max(bx,ex);
  }
}
int range(double p,double q,double r){
  return (q<r?q:r)<p&&p<(q<r?r:q);
}
int rangea(double p,double q,double r){
  if(q*r<0&&fabs(q)+fabs(r)>M_PI){
    p+=2*M_PI*(p<0);
    q+=2*M_PI*(q<0);
    r+=2*M_PI*(r<0);
  }
  return range(p,q,r);
}
int pit(int ax,int ay,int bx,int by,int cx,int cy,int px,int py){
  if(rangea(atan2(ay-py,ax-px),atan2(ay-by,ax-bx),atan2(ay-cy,ax-cx))){
    if(rangea(atan2(by-py,bx-px),atan2(by-ay,bx-ax),atan2(by-cy,bx-cx))){
      return 1;
    }
  }
  return 0;
}
int main(){
  int i;
  int ac[3],ax[3],ay[3],cx,cy,cr;
  while(cin>>ax[0]>>ay[0]&&ax[0]&&ay[0]){
    for(i=1;i<3;i++)
      cin>>ax[i]>>ay[i];
    cin>>cx>>cy>>cr;
    for(i=0;i<3;i++)
      ac[i]=(ax[i]-cx)*(ax[i]-cx)+(ay[i]-cy)*(ay[i]-cy)>cr*cr;
    if(0){
    }else if(ac[0]&ac[1]&ac[2]){
      for(i=0;i<3;i++)
	ac[i]=g(ax[i],ay[i],ax[(i+1)%3],ay[(i+1)%3],cx,cy,cr);
      if(0){
      }else if(ac[0]==0&&ac[1]==0&&ac[2]==0){
	if(pit(ax[0],ay[0],ax[1],ay[1],ax[2],ay[2],cx,cy))
	  cout<<"a"<<endl;
	else
	  cout<<"d"<<endl;
      }else if(ac[0]==1||ac[1]==1||ac[2]==1){
	cout<<"c"<<endl;
      }else{
	if(pit(ax[0],ay[0],ax[1],ay[1],ax[2],ay[2],cx,cy))
	  cout<<"a"<<endl;
	else
	  cout<<"c"<<endl;
      }
    }else if(ac[0]|ac[1]|ac[2]){
      cout<<"c"<<endl;
    }else{
      cout<<"b"<<endl;
    }
  }
  return 0;
}