#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<ll,ll> mp;
#define inf 1e9
#define EPS 1e-10
struct point{
	double x,y;
	void make(){
		cin>>x>>y;
	}
	point(){};
	point(double x,double y):x(x),y(y){};
	point operator + (point &p) { return point(x+p.x,y+p.y)  ; }
	point operator - (point &p) { return point(x-p.x,y-p.y)  ; }
	double norm() { return x*x+y*y;}
	double abs() { return sqrt(norm()) ;}
};
struct line{
	point s,e;
};

double cross(point a,point b){
	return a.x*b.y-a.y*b.x;
}
double dot(point a,point b){
	return a.x*b.x+a.y*b.y;
}

struct circle{
	point p;
	double r;
	void make(){
		p.make();
		cin>>r;
	}
};

double abs(point a){
	return a.abs();
}
double distance(line l,point p){
	point tmp = l.e-l.s;
	if(dot(tmp,p-l.s) < EPS) return abs(p-l.s);
	if(dot(l.s-l.e,p-l.e) < EPS ) return abs(p-l.e);
	return abs(cross(l.e-l.s,p-l.s ) / abs(l.e-l.s) );
}


int main(){
	while(1){
		point p[3];
		p[0].make();
		if(p[0].x==0 && p[0].y==0 )break;
		p[1].make();
		p[2].make();
		circle c;
		c.make();
		double d[3];
		double l[3];
		double r = c.r;
		for(int i=0;i<3;i++){
			point dis = p[i]-c.p;
			d[i] = dis.abs();
			line lt;
			lt.s = p[(i+1)%3];
			lt.e = p[(i+2)%3];
			l[i] = distance(lt,c.p);
		}
		double area = abs(cross(p[2]-p[0],p[1]-p[0]) );
		double area2 = 0.0;
		for(int i=0;i<3;i++){
			area2+= abs( cross(p[i]-c.p, p[(i+1)%3]-c.p ) );
		}
		
		if( r <= l[0]+EPS && r <= l[1]+EPS && r <= l[2]+EPS && area2 <= area + EPS ){
		//    cout<<l[0]<<' '<<l[1]<<' '<<l[2]<<endl;
			cout<<'a'<<endl;
		}else if(d[0] <= r+EPS && d[1] <= r+EPS && d[2] <= r+EPS){
			cout<<'b'<<endl;
		}else if(d[0] > r && d[1] > r&& d[2] >r && l[0]>r&&l[1]>r&&l[2]>r){
			cout<<'d'<<endl;
		}else {
			cout<<'c'<<endl;
		}



	}
	return 0;
}

