#include <iostream>
#include <complex>
#include <sstream>
#include <string>
#include <algorithm>
#include <deque>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <vector>
#include <set>
#include <limits>
#include <cstdio>
#include <cctype>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <ctime>
using namespace std;
#define REP(i, j) for(int i = 0; i < (int)(j); ++i)
#define FOR(i, j, k) for(int i = (int)(j); i < (int)(k); ++i)
#define SORT(v) sort((v).begin(), (v).end())
#define REVERSE(v) reverse((v).begin(), (v).end())
#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
#define diff(P, i) (next(P, i) - curr(P, i))
const double EPS = 1e-8;
#define EQ(a,b) (abs((a)-(b)) < EPS)
#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
typedef complex<double> P;

struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};

double cross(const P& a, const P& b) { return imag(conj(a)*b); }
double dot(const P& a, const P& b) { return real(conj(a)*b); }

P projection(const L &l, const P &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 distanceLP(const L &l, const P &p) { return abs(p - projection(l, p)); }

int ccw(P a, P b, P c) {
  b -= a; c -= a;
  if (cross(b, c) > 0)   return +1;       // counter clockwise
  if (cross(b, c) < 0)   return -1;       // clockwise
  if (dot(b, c) < 0)     return +2;       // c--a--b on line
  if (norm(b) < norm(c)) return -2;       // a--b--c on line
  return 0;
}

//-1 ???????????????
//0 ??\??????
//1 ???????????§????????????
//2 ???????????§????????????
int intersectSC(const L &s, const C &c) {
  int ins = 0;
  for(int i = 0; i < 2; i++ ) {
    if (abs(s[i]-c.p)<c.r) ins++;
    else if (EQ(abs(s[i]-c.p), c.r)) return 0;
  }
  if (ins == 2) return -1;
  if (ins == 1) return 1;
  double d = distanceLP(s, c.p);
  if (d-c.r > EPS) return -1;
  P nor=(s[0]-s[1]) * P(0, 1);
  if (ccw(c.p, c.p+nor, s[0]) * ccw(c.p, c.p+nor, s[1]) < 0) return 2;
  return -1;
}

enum { OUT, ON, IN };
int contains(const vector<P> &g, const P &p) {
  bool in = false;
  for (int i = 0; i < g.size(); ++i) {
    P a = curr(g,i) - p, b = next(g,i) - p;
    if (imag(a) > imag(b)) swap(a, b);
    if (imag(a) <= 0 && 0 < imag(b))
      if (cross(a, b) < 0) in = !in;
    if (cross(a, b) == 0 && dot(a, b) <= 0) return ON;
  }
  return in ? IN : OUT;
}

bool inputP(P &p){
  int x, y; cin >>x >>y;
  if(x == 0 && y == 0) return false;
  p = P(x, y);
  return true;
}

char solve(vector<P> &t, P c, int r){
    double d[3];
    REP(i, 3) d[i] = abs(c - t[i]);
    if(d[0] >= r && d[1] >= r && d[2] >= r && contains(t, c) == IN) return 'a';
    if(d[0] <= r && d[1] <= r && d[2] <= r) return 'b';
    REP(i, 3) if(intersectSC(L(t[i], next(t, i)), C(c, r)) > -1) return 'c';
    return 'd';
}

int main(){
  vector<P> t(3);
  P c;
  int r;
  while(inputP(t[0])){
    FOR(i, 1, 3) inputP(t[i]);
    inputP(c); cin >>r;
    cout <<solve(t, c, r) <<endl;
  }
  return 0;
}