#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <ctime>
#include <queue>
#include <stack>
#include <algorithm>
#include <list>
#include <vector>
#include <set>
#include <map>
#include <iostream>
#include <deque>
#include <complex>
#include <string>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <valarray>
#include <iterator>
using namespace std;
typedef long long int ll;
typedef unsigned int uint;
typedef unsigned char uchar;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

#define REP(i,x) for(int i=0;i<(int)(x);i++)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++)
#define ALL(container) container.begin(), container.end()
#define RALL(container) container.rbegin(), container.rend()
#define SZ(container) ((int)container.size())
#define mp(a,b) make_pair(a, b)
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T> ostream& operator<<(ostream &os, const vector<T> &t) {
os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os;
}
template<class T> ostream& operator<<(ostream &os, const set<T> &t) {
os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os;
}
template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";}
template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first-t.first, s.second-t.second);}

const int INF = 1<<28;
const double EPS = 1e-8;
const int MOD = 1000000007;

namespace geom{
#define X real()
#define Y imag()
#define at(i) ((*this)[i])
#define SELF (*this)

	enum {TRUE = 1, FALSE = 0, BORDER = -1};
	typedef int BOOL;
	typedef double R;
	inline int sig(const R &x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }
	inline BOOL less(const R &x, const R &y) {return sig(x-y) ? x < y : BORDER;}
	typedef complex<R> P;
	istream& operator>>(istream &is, P &p) {
		R x, y;
		is >> x >> y;
		p = P(x, y);
		return is;
	}
	inline R norm(const P &p){return p.X*p.X+p.Y*p.Y;}
	inline R inp(const P& a, const P& b){return (conj(a)*b).X;}
	inline R outp(const P& a, const P& b){return (conj(a)*b).Y;}
	inline P unit(const P& p){return p/abs(p);}
	inline P proj(const P &s, const P &t){return t*inp(s, t)/norm(t);}

	struct L : public vector<P>{	// line
		L(const P &p1, const P &p2){this->push_back(p1);this->push_back(p2);}
		P dir()const {return SELF[1] - SELF[0];}
		friend istream& operator>>(istream &is, L &l) {
			P p1, p2;
			is >> p1 >> p2;
			l = L(p1, p2);
			return is;
		}
		friend inline P proj(const P &s, const L &t){return t[0] + proj(s-t[0], t[1]-t[0]);}
		BOOL online(const P &p)const {return !sig(outp(p-SELF[0], dir()));}
		R distance(const P &p)const {return abs(outp(dir(), p - SELF[0])) / abs(dir());}
	};
	struct S : public L{	// segment
		S(const P &p1, const P &p2):L(p1, p2){}
		BOOL online(const P &p){
			if(!sig(abs(p - SELF[0])) || !sig(abs(p - SELF[1]))) return BORDER;
			return !sig(abs(SELF[0]-p) + abs(SELF[1] - p) - abs(SELF[0] - SELF[1]));
		}
		R distance(const P &p)const {
			if(inp(p-SELF[0],  dir()) < EPS) return abs(p - SELF[0]);
			if(inp(p-SELF[1], -dir()) < EPS) return abs(p - SELF[1]);
			return L::distance(p);
		}
	};

	struct C : public P{
		R r;
		friend istream& operator>>(istream &is, C &c) {
			operator>>(is, (P &)c);
			is >> c.r;
			return is;
		}
		BOOL inside(const P& p)const { return !sig(abs(p-SELF) - r) ? BORDER : abs(p-SELF) < r - EPS;}
		friend inline BOOL cc_intersect(const C &a, const C &b){
			if(!sig(abs(a-b) - (a.r+b.r) || !sig(abs(a-b) - abs(a.r - b.r)))) return BORDER;
			return abs(a-b)<a.r+b.r && abs(a-b)>abs(a.r - b.r);
		}
		friend inline int cl_intersect(const C &c, const L &l){
			return less(l.distance(c), c.r);
		}
		friend inline int cs_intersect(const C &c, const S &s){
			if(c.inside(s[0]) != FALSE && c.inside(s[1]) != FALSE) return c.inside(s[0]) | c.inside(s[1]);
			return less(s.distance(c), c.r);
		}
	};
	
	struct G : public vector<P>{
		S edge(int i)const {return S(at(i), at((i+1)%size()));}
		BOOL contains(const P &p)const {
			R sum = .0;
			REP(i, size()){
				if(S(at(i), at((i+1)%size())).online(p)) return BORDER;	// online
				sum += arg((at(i) - p) / (at((i+1)%size()) - p));
			}
			return !!sig(sum);
		}
		
		BOOL contains(const C &c)const {
			if(!contains((P)c)) return FALSE;
			R sum = .0;
			int res = TRUE;
			REP(i, size()){
				if(c.inside(at(i)) == TRUE || less(edge(i).distance(c), c.r) == TRUE) return FALSE;
				else res |= c.inside(at(i)) | less(edge(i).distance(c), c.r);
			}
			return res;
		}
		
		R area(){
			R sum = 0;
			REP(i, size()) sum += outp(at(i), at((i+1)%size()));
			return abs(sum / 2.);
		}
	};
#undef SELF
#undef at
};
using namespace geom;

int n;

char check(const C& c, const G &g){
	if(g.contains(c)) return 'a';
	int f = 1;
	REP(i, 3) if(!c.inside(g[i])) f = 0;
	if(f) return 'b';
	REP(i, 3) if(cs_intersect(c, g.edge(i))) return 'c';
	return 'd';
}

int main(){
	ios::sync_with_stdio(false);
	while(1){
		G g;
		C c;
		REP(i, 3){
			P p;
			cin >> p;
			if(p.X == 0) return 0;
			g.push_back(p);
		}
		cin >> c;
		cout << check(c, g) << endl;
	}
	return 0;
}

Measured memory_bytes: 1304