#include<cmath>
#include<algorithm>
#include<iostream>
#include<vector>
#include<string>
#include<climits>
#include<cfloat>

using namespace std;

double EPS = 1e-10;
const double PI = acos(-1);

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);
}

bool operator == ( const point &p ) const {
return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
}
};

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); }


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 is_point_on_line(point a, point b, point c) {
return cross(b-a, c-a)==0.0 &&
(dot(b-a, c-a) > -EPS) &&
(dot(a-b, c-b) > -EPS);
}

int is_intersected_ls(point a1, point a2, point b1, point b2) {

if(cross(a1-a2,b1-b2)==0){
return is_point_on_line(a1,a2,b1) || is_point_on_line(a1,a2,b2)
|| is_point_on_line(b1,b2,a1) || is_point_on_line(b1,b2,a2);
}
else {
return ( cross(a2-a1, b1-a1) * cross(a2-a1, b2-a1) < EPS ) &&
( cross(b2-b1, a1-b1) * cross(b2-b1, a2-b1) < EPS );
}

}

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;
}

int inside(point p, vector<point> ps, int n){
point a,b;
a=b=p;
b.x=DBL_MAX;
ps.push_back(ps[0]);
double ymx=-DBL_MAX,ymn=DBL_MAX;
for(int i=0;i ymx=max(ymx,ps[i].y);
ymn=min(ymn,ps[i].y);
}
if(a.y<=ymn||a.y>=ymx)return 0;

for(int i=0;i<n;i++){
if(is_point_on_line(ps[i],ps[i+1],p))return 1;
}

int cnt1=0;
for(int i=0;i<n;i++)
if(is_point_on_line(a,b,ps[i]))cnt1++;

int cnt=0;
for(int i=0;i<n;i++)
if(is_intersected_ls(ps[i],ps[i+1],a,b))cnt++;

return (cnt-cnt1)%2;
}

int crossCP(vector<point> t, circle C){

double ans=0;
int tsz=t.size();

for(int i=0;i<tsz;i++){
double tmp=dist(t[i],C.p);
if(tmp>ans)ans=tmp;
}

if(C.r>=ans)return 2;

int res1=inside(C.p,t,tsz);
double res2=DBL_MAX;

t.push_back(t[0]);

for(int i=0;i<tsz;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 else return 3;
}

int main(void){
point p;
vector t;
circle C;
string ans="zabcd";

while(true){
t.clear();
for(int i=0;i<3;i++){
cin >> p.x >> p.y;
if(p.x==0 && p.y==0)return 0;
t.push_back(p);
}
cin >> C.p.x >> C.p.y >> C.r;

int res=crossCP(t,C);
cout << ans[res] << endl;
}
return 0;
}