Go: package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)

func main() {
	for scanner.Scan() {
		buf0 := strings.Split(scanner.Text(), " ")
		input0 := make([]int, 2)
		for i := range input0 {
			input0[i], _ = strconv.Atoi(buf0[i])
		}
		if input0[0] == 0 && input0[1] == 0 {
			break
		}
		a, b := input0[0], input0[1]
		scanner.Scan()
		buf1 := strings.Split(scanner.Text(), " ")
		input1 := make([]int, 2)
		for i := range input1 {
			input1[i], _ = strconv.Atoi(buf1[i])
		}
		c, d := input1[0], input1[1]
		scanner.Scan()
		buf2 := strings.Split(scanner.Text(), " ")
		input2 := make([]int, 2)
		for i := range input2 {
			input2[i], _ = strconv.Atoi(buf2[i])
		}
		e, f := input2[0], input2[1]
		scanner.Scan()
		buf3 := strings.Split(scanner.Text(), " ")
		input3 := make([]int, 2)
		for i := range input3 {
			input3[i], _ = strconv.Atoi(buf3[i])
		}
		g, h := input3[0], input3[1]
		scanner.Scan()
		r, _ := strconv.Atoi(scanner.Text())
		if (a-g)*(a-g)+(b-h)*(b-h) <= r*r && (c-g)*(c-g)+(d-h)*(d-h) <= r*r && (e-g)*(e-g)+(f-h)*(f-h) <= r*r {
			fmt.Println("b")
		} else if dist(a, b, c, d, g, h) > float64(r)-0.000001 && dist(a, b, e, f, g, h) > float64(r)-0.000001 && dist(e, f, c, d, g, h) > float64(r)-0.000001 && inclusive(a, b, c, d, e, f, g, h) {
			fmt.Println("a")
		} else if CL_intersect(a, b, c, d, g, h, r) || CL_intersect(a, b, e, f, g, h, r) || CL_intersect(e, f, c, d, g, h, r) {
			fmt.Println("c")
		} else {
			fmt.Println("d")
		}
	}
}

func CL_intersect(ax, ay, bx, by, cx, cy, r int) bool {
	acx := cx - ax
	acy := cy - ay
	bcx := cx - bx
	bcy := cy - by
	abx := bx - ax
	aby := by - ay
	if acx*acx+acy*acy >= r*r || bcx*bcx+bcy*bcy >= r*r {
		if abx*acx+aby*acy < 0 {
			if acx*acx+acy*acy <= r*r {
				return true
			}
		} else {
			if abx*acx+aby*acy > abx*abx+aby*aby {
				if bcx*bcx+bcy*bcy <= r*r {
					return true
				}
			} else if acx*acx+acy*acy-(abx*acx+aby*acy)*(abx*acx+aby*acy)/(abx*abx+aby*aby) <= r*r {
				return true
			}
		}
	}
	return false
}

func inclusive(ax, ay, bx, by, cx, cy, px, py int) bool {
	ok1 := true
	ok2 := true
	if (bx-ax)*(py-ay)-(px-ax)*(by-ay) < 0 {
		ok1 = false
	}
	if (bx-ax)*(py-ay)-(px-ax)*(by-ay) > 0 {
		ok2 = false
	}
	if (cx-bx)*(py-by)-(px-bx)*(cy-by) < 0 {
		ok1 = false
	}
	if (cx-bx)*(py-by)-(px-bx)*(cy-by) > 0 {
		ok2 = false
	}
	if (ax-cx)*(py-cy)-(px-cx)*(ay-cy) < 0 {
		ok1 = false
	}
	if (ax-cx)*(py-cy)-(px-cx)*(ay-cy) > 0 {
		ok2 = false
	}
	return ok1 || ok2
}

func dist(ax, ay, bx, by, px, py int) float64 {
	dx := float64(bx - ax)
	dy := float64(by - ay)
	A := float64(dx*dx + dy*dy)
	B := dx*float64(ax-px) + dy*float64(ay-py)
	t := -B / A
	if t < 0 {
		t = 0
	}
	if t > 1 {
		t = 1
	}
	tx := float64(ax) + dx*t
	ty := float64(ay) + dy*t
	return math.Sqrt((float64(px)-tx)*(float64(px)-tx) + (float64(py)-ty)*(float64(py)-ty))
}

C++: #include <cmath>
#include <cstdio>
#include <complex>
#include <algorithm>
#define Point complex<long double>
#define px real()
#define py imag()
using namespace std;
// ------ Classes ------ //
class Segment {
public:
	Point p1, p2;
	Segment(Point p1_, Point p2_) : p1(p1_), p2(p2_) {};
	Segment(long double p1x, long double p1y, long double p2x, long double p2y) : p1(Point(p1x, p1y)), p2(Point(p2x, p2y)) {};
	friend bool operator==(const Segment& s1, const Segment& s2) { return (s1.p1 == s2.p1 && s1.p2 == s2.p2) || (s1.p1 == s2.p2 && s1.p2 == s2.p1); }
	friend bool operator!=(const Segment& s1, const Segment& s2) { return !(s1 == s2); }
};
class Line {
public:
	Point p1, p2;
	Line(Point p1_, Point p2_) : p1(p1_), p2(p2_) {};
	Line(long double p1x, long double p1y, long double p2x, long double p2y) : p1(Point(p1x, p1y)), p2(Point(p2x, p2y)) {};
	friend bool operator==(const Line& s1, const Line& s2) { return (s1.p1 == s2.p1 && s1.p2 == s2.p2) || (s1.p1 == s2.p2 && s1.p2 == s2.p1); }
	friend bool operator!=(const Line& s1, const Line& s2) { return !(s1 == s2); }
};
// ------ Functions ------ //
long double dot(const Point& a, const Point& b) { return a.px * b.px + a.py * b.py; }
long double crs(const Point& a, const Point& b) { return a.px * b.py - a.py * b.px; }
int ccw(Point p0, Point p1, Point p2) {
	Point a = p1 - p0, b = p2 - p0;
	if (crs(a, b) > 1e-10) return 1;
	if (crs(a, b) < -1e-10) return -1;
	if (dot(a, b) < -1e-10) return 2;
	if (norm(a) < norm(b)) return - 2;
	return 0;
}
bool its(Point p1, Point p2, Point p3, Point p4) {
	return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 && ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);
}
bool its(Segment s1, Segment s2) {
	return its(s1.p1, s1.p2, s2.p1, s2.p2);
}
long double dst(const Point& a, const Point& b) {
	return sqrtl((a.px - b.px) * (a.px - b.px) + (a.py - b.py) * (a.py - b.py));
}
long double dst(const Line& a, const Point& b) {
	return abs(crs(a.p2 - a.p1, b - a.p1) / abs(a.p2 - a.p1));
}
long double dst(const Segment& a, const Point& b) {
	if (dot(a.p2 - a.p1, b - a.p1) < 0.0) return abs(b - a.p1);
	if (dot(a.p1 - a.p2, b - a.p2) < 0.0) return abs(b - a.p2);
	return abs(crs(a.p2 - a.p1, b - a.p1) / abs(a.p2 - a.p1));
}
long double dst(const Segment& a, const Segment& b) {
	if (its(a, b)) return 0;
	return min( { dst(a, b.p1), dst(a, b.p2), dst(b, a.p1), dst(b, a.p2) });
}
int xa, ya, xb, yb, xc, yc, xd, yd, r;
int main() {
	while(true) {
		scanf("%d%d", &xa, &ya);
		if(xa == 0 && ya == 0) break;
		scanf("%d%d%d%d%d%d%d", &xb, &yb, &xc, &yc, &xd, &yd, &r);
		Point p1(xa, ya), p2(xb, yb), p3(xc, yc), p4(xd, yd);
		Segment s1(p1, p2), s2(p2, p3), s3(p3, p1);
		if(dst(s1, p4) <= r && dst(s2, p4) <= r && dst(s3, p4) <= r) printf("a\n");
		else if(dst(p1, p4) <= r && dst(p2, p4) <= r && dst(p3, p4) <= r) printf("b\n");
		else if(dst(p1, p4) <= r || dst(p2, p4) <= r || dst(p3, p4) <= r) printf("c\n");
		else printf("d\n");
	}
	return 0;
}