#include <stdio.h>
#include <iostream>
#include <vector>
#include <list>
#include <cmath>
#include <fstream>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <complex>
#include <iterator>
#include <cstdlib>
#include <cstring>
#include <sstream>

using namespace std;

#define EPS (1e-10)
#define EQ(a,b) (abs((a) - (b)) < EPS)
#define EQV(a,b) (EQ((a).real(),(b).real()) && EQ((a).imag(),(b).imag()))

typedef complex<double> P;
typedef long long ll;

const int MAX_SIZE = 10000;

// àÏ
double dot(P a, P b) {
  return (a.real() * b.real() + a.imag() * b.imag());
}
// OÏ
double cross(P a, P b) {
  return (a.real() * b.imag() - a.imag() * b.real());
}
// _cª¼üabãÉ é©È¢©
int is_point_on_line(P a, P b, P c) {
  return EQ( cross(b-a, c-a), 0.0 );
}
// 2¼üÌ¼s»è
int is_orthogonal(P a1, P a2, P b1, P b2) {
  return EQ( dot(a1-a2, b1-b2), 0.0 );
}
// 2¼üÌ½s»è
int is_parallel(P a1, P a2, P b1, P b2) {
  return EQ( cross(a1-a2, b1-b2), 0.0 );
}
// _a,bðÊé¼üÆ_cÌÔÌ£
double distance_l_p(P a, P b, P c) {
  return abs(cross(b-a, c-a)) / abs(b-a);
}
// _a,bð[_Æ·éüªÆ_cÆÌ£
double distance_ls_p(P a, P b, P c) {
  if ( dot(b-a, c-a) < EPS ) return abs(c-a);
  if ( dot(a-b, c-b) < EPS ) return abs(c-b);
  return abs(cross(b-a, c-a)) / abs(b-a);
}
// a1,a2ð[_Æ·éüªÆb1,b2ð[_Æ·éüªÌð·»è
int is_intersected_ls(P a1, P a2, P b1, P b2) {
  return ( cross(a2-a1, b1-a1) * cross(a2-a1, b2-a1) < EPS ) &&
         ( cross(b2-b1, a1-b1) * cross(b2-b1, a2-b1) < EPS );
}
// a1,a2ð[_Æ·éüªÆb1,b2ð[_Æ·éüªÌð_vZ
P intersection_ls(P a1, P a2, P b1, P b2) {
  P b = b2-b1;
  double d1 = abs(cross(b, a1-b1));
  double d2 = abs(cross(b, a2-b1));
  double t = d1 / (d1 + d2);

  return a1 + (a2-a1) * t;
}
// a1,a2ðÊé¼üÆb1,b2ðÊé¼üÌð·»è
int is_intersected_l(P a1, P a2, P b1, P b2) {
  return !EQ( cross(a1-a2, b1-b2), 0.0 );
}
// a1,a2ðÊé¼üÆb1,b2ðÊé¼üÌð_vZ
P intersection_l(P a1, P a2, P b1, P b2) {
  P a = a2 - a1; P b = b2 - b1;
  return a1 + a * cross(b, b1-a1) / cross(b, a);
}
/*
~üÆüªÌð·»è
*/
bool isCircleCrossLine(P a,P b,P c,double r){
	double d1 = abs(a-c);
	double d2 = abs(b-c);
	if(d1<r&&d2<r){
		return false;
	}
	double d = distance_ls_p(a,b,c);
	if(EQ(d,r)||d<r){
		return true;
	}
	else
		return false;
}
// Op`ÌàÉ_ª é©Ç¤©
// OÏÌ³ª·×Ä¯¶ÈçàÉ_ è
bool isInTriangle(P p1,P p2,P p3,P s){
	P a=p1-s;
	P b=p2-s;
	P c=p3-s;
	return ((((cross(a,b)>0))&&(cross(b,c)>0))&&(cross(c,a)>0))
		||(cross(a,b)<0&&cross(b,c)<0&&cross(c,a)<0);
}

struct Circle{
	double x,y,r;
};

struct Triangle{
	complex<double> p[3];
};

int main(){

	Circle c;
	Triangle t;
	while(1){
		bool f=false;
		for(int i = 0; i < 3; i++){
			double x,y;
			cin>>x>>y;
			if(x==0&&y==0){
				f=true;
				break;
			}
			t.p[i]=complex<double>(x,y);
		}
		if(f)
			break;
		cin>>c.x>>c.y>>c.r;
		// vZ
		// Op`ð\¬·éR_ªÆàÉ~ÌàÉ éÈçÎAOp`Í~ÉÜÜêé
		if(((t.p[0].real()-c.x)*(t.p[0].real()-c.x)+(t.p[0].imag()-c.y)*(t.p[0].imag()-c.y)<c.r*c.r&&!EQ((t.p[0].real()-c.x)*(t.p[0].real()-c.x)+(t.p[0].imag()-c.y)*(t.p[0].imag()-c.y),c.r*c.r))
			&&((t.p[1].real()-c.x)*(t.p[1].real()-c.x)+(t.p[1].imag()-c.y)*(t.p[1].imag()-c.y)<c.r*c.r&&!EQ((t.p[1].real()-c.x)*(t.p[1].real()-c.x)+(t.p[1].imag()-c.y)*(t.p[1].imag()-c.y),c.r*c.r))
			&&((t.p[2].real()-c.x)*(t.p[2].real()-c.x)+(t.p[2].imag()-c.y)*(t.p[2].imag()-c.y)<c.r*c.r&&!EQ((t.p[2].real()-c.x)*(t.p[2].real()-c.x)+(t.p[2].imag()-c.y)*(t.p[2].imag()-c.y),c.r*c.r))
			){
				cout<<"b"<<endl;
		}
		// 3üªÆ~ÌSÌ£ªÇêàrÈãÅ èA©Â~Ì_ªOp`ÌàÉ¶Ý·éÈçÎA~ÍOp`ÉÜÜêé
		else if((distance_ls_p(t.p[0],t.p[1],P(c.x,c.y))>c.r&&!EQ(distance_ls_p(t.p[0],t.p[1],P(c.x,c.y)),c.r))
			&&(distance_ls_p(t.p[1],t.p[2],P(c.x,c.y))>c.r&&!EQ(distance_ls_p(t.p[1],t.p[2],P(c.x,c.y)),c.r))
			&&(distance_ls_p(t.p[2],t.p[0],P(c.x,c.y))>c.r&&!EQ(distance_ls_p(t.p[2],t.p[0],P(c.x,c.y)),c.r))
			&&isInTriangle(t.p[0],t.p[1],t.p[2],P(c.x,c.y))
			){
				cout<<"a"<<endl;
		}
		// OüªÆ~ÌSÌ£ªÇêàræè¨¨«­A©ÂO_Æ~ÌSÌ£ªræèå«­A©Â~Ì_ªOp`ÌàÉ¶ÝµÈ¢ê
		// ¤Êªðà½È¢
		else if((distance_ls_p(t.p[0],t.p[1],P(c.x,c.y))>c.r||EQ(distance_ls_p(t.p[0],t.p[1],P(c.x,c.y)),c.r))
			&&(distance_ls_p(t.p[1],t.p[2],P(c.x,c.y))>c.r||EQ(distance_ls_p(t.p[1],t.p[2],P(c.x,c.y)),c.r))
			&&(distance_ls_p(t.p[2],t.p[0],P(c.x,c.y))>c.r||EQ(distance_ls_p(t.p[2],t.p[0],P(c.x,c.y)),c.r))
			&&(!isInTriangle(t.p[0],t.p[1],t.p[2],P(c.x,c.y)))
			&&((t.p[0].real()-c.x)*(t.p[0].real()-c.x)+(t.p[0].imag()-c.y)*(t.p[0].imag()-c.y)>c.r*c.r||EQ((t.p[0].real()-c.x)*(t.p[0].real()-c.x)+(t.p[0].imag()-c.y)*(t.p[0].imag()-c.y),c.r*c.r))
			&&((t.p[1].real()-c.x)*(t.p[1].real()-c.x)+(t.p[1].imag()-c.y)*(t.p[1].imag()-c.y)>c.r*c.r||EQ((t.p[1].real()-c.x)*(t.p[1].real()-c.x)+(t.p[1].imag()-c.y)*(t.p[1].imag()-c.y),c.r*c.r))
			&&((t.p[2].real()-c.x)*(t.p[2].real()-c.x)+(t.p[2].imag()-c.y)*(t.p[2].imag()-c.y)>c.r*c.r||EQ((t.p[2].real()-c.x)*(t.p[2].real()-c.x)+(t.p[2].imag()-c.y)*(t.p[2].imag()-c.y),c.r*c.r))
			){

				cout<<"d"<<endl;
		}
		// ~ªOp`ÉÜÜê¸A©ÂO_ÆàÉ~ÌOÉ éÈçÎAOp`Æ~Ì¤ÊªÍÈ¢
		//else if((t.p[0].real()-c.x)*(t.p[0].real()-c.x)+(t.p[0].imag()-c.y)*(t.p[0].imag()-c.y)>c.r*c.r
		//	&&(t.p[1].real()-c.x)*(t.p[1].real()-c.x)+(t.p[1].imag()-c.y)*(t.p[1].imag()-c.y)>c.r*c.r
		//	&&(t.p[2].real()-c.x)*(t.p[2].real()-c.x)+(t.p[2].imag()-c.y)*(t.p[2].imag()-c.y)>c.r*c.r){
		//		cout<<"d"<<endl;
		//}
		else{
			cout<<"c"<<endl;
		}
	}

	return 0;
}