#include <bits/stdc++.h>
using namespace std;

typedef complex<double> C;

double ip(C a, C b){
    return a.real() * b.real() + a.imag() * a.imag();
}

double dist_lc(C p, double a, double b, double c){
    return abs(a * p.real() + b * p.imag() + c) / abs(p);
}

int main(){
    C p1, p2, p3, pr;
    double r;
    while(true){
        int s, t;
        scanf("%d%d", &s, &t);
        if(s == 0 && t == 0) break;
        p1.real(s); p1.imag(t);
        scanf("%d%d", &s, &t);
        p2.real(s); p2.imag(t);
        scanf("%d%d", &s, &t);
        p3.real(s); p3.imag(t);
        scanf("%d%d", &s, &t);
        pr.real(s); pr.imag(t);
        scanf(" %lf", &r);
        if(abs(p1 - pr) <= r && abs(p2 - pr) <= r && abs(p3 - pr) <= r){
            puts("b");
            continue;
        }
        double a = (p1-p2).real(), b = (p1-p2).imag();
        double c = (p2-p3).real(), d = (p2-p3).imag();
        double e = (p3-p1).real(), f = (p3-p1).imag();
        bool flg1 = abs(b * pr.real() - a * pr.imag() - b * pr.real() + a * pr.imag())/abs(pr) <= r;
        bool flg2 = abs(d * pr.real() - c * pr.imag() - d * pr.real() + c * pr.imag())/abs(pr) <= r;
        bool flg3 = abs(f * pr.real() - e * pr.imag() - f * pr.real() + e * pr.imag())/abs(pr) <= r;
        if(flg1 || flg2 || flg3){
            puts("a");
            continue;
        }
        flg1 = abs(pr - p1) <= r;
        flg2 = abs(pr - p2) <= r;
        flg3 = abs(pr - p3) <= r;
        if(flg1 || flg2 || flg3){
            puts("c");
            continue;
        }
        flg1 = dist_lc(pr, b, -a, -b * p1.real() + a * p1.imag()) <= r &&
               ip(p1-p2, pr-p2) >= 0 && ip(p2-p1, pr-p1) >= 0;
        flg2 = dist_lc(pr, d, -c, -d * p2.real() + b * p2.imag()) <= r &&
               ip(p2-p3, pr-p3) >= 0 && ip(p3-p2, pr-p2) >= 0;
        flg3 = dist_lc(pr, f, -e, -f * p3.real() + f * p3.imag()) <= r &&
               ip(p3-p1, pr-p1) >= 0 && ip(p1-p3, pr-p3) >= 0;
        if(flg1 || flg2 || flg3){
            puts("c");
            continue;
        }
        puts("d");
    }
    return 0;
}