#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
typedef long long ll;
using namespace std;
 
struct Pos{
    double x,y;
    Pos(double x,double y) : x(x) , y(y) {}
    Pos(){}
};
 
struct Triangle{
    Pos pos[3];
};
struct Circle{
    Pos pos;
    double r;
};
 
static const double kyuriEPS = 1e-1;
typedef std::complex<double> myPoint;
double dot(const myPoint& a, const myPoint& b) {return real(conj(a)*b);}
struct myL : public std::vector<myPoint> {
    myL(const myPoint &a, const myPoint &b) {push_back(a); push_back(b);}
};
 
bool intersectSP(const myL &s, const myPoint &p) {
    return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < kyuriEPS;
} 
myPoint projection(const myL &l, const myPoint &p) {
    double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);return l[0] + t*(l[0]-l[1]);
}
 
double distanceSP(const myL &s, const myPoint &p) {
    const myPoint r = projection(s, p);
    if (intersectSP(s, r)) return abs(r - p);
    return std::min(abs(s[0] - p), abs(s[1] - p));
}
//ct
int judgeHit(const Circle &c,const Triangle &t){
    int counter = 0 , ctt = 0;
    for(int i = 0 ; i < 3 ; i++){
        if( abs(myPoint(c.pos.x,c.pos.y)-myPoint(t.pos[i].x,t.pos[i].y)) <= c.r ){
            ctt++;
        }
    }
    if( ctt == 3 ) return 1;
	if( ctt >= 1 ) return 2;
    for(int i = 0 ; i < 3 ; i++){
        double dist = distanceSP(myL(myPoint(t.pos[i].x,t.pos[i].y),myPoint(t.pos[(i+1)%3].x,t.pos[(i+1)%3].y)),myPoint(c.pos.x,c.pos.y));
        if( dist <= c.r - kyuriEPS ){
            counter++;
        }
    }
    if( counter >= 1 ) return 2;
     
	double tS2 = fabs( (t.pos[1].x-t.pos[0].x)*(t.pos[2].y-t.pos[0].y) - (t.pos[1].y-t.pos[0].y)*(t.pos[2].x-t.pos[0].x) );
	
	// a.pos[i] on B
	double area = 0;
	for(int j = 0 ; j < 3 ; j++){
		area += fabs( (t.pos[j].x-c.pos.x)*(t.pos[(j+1)%3].y-c.pos.y) - (t.pos[j].y-c.pos.y)*(t.pos[(j+1)%3].x-c.pos.x) );
	}
	//std::cout << area << " " << tS2 << std::endl;
	
	if( fabs( fabs(area) - tS2 ) == 0 ) return 0; 	
	
	return 3;
}
 
int main(){
    Triangle t;
    Circle c;
    while(cin >> t.pos[0].x >> t.pos[0].y && (t.pos[0].x||t.pos[0].y)){
        for(int i = 1 ; i < 3 ; i++)
            cin >> t.pos[i].x >> t.pos[i].y;
        cin >> c.pos.x >> c.pos.y >> c.r;
        cout << (char)('a'+judgeHit(c,t)) << endl;
    }
}