Language: C

#define hypot _hypot
float q;
A,B,C,D,E,F,R;
M(a,b,c,d,e,f){
	e=c-a;
	f=d-b;
	q=fabs(-f*a+e*b)/hypot(e,f);
	if(a*e+b*f<0&&c*e+d*f>0&&q<=R)
		if(q<R)
			return 2;
		else
			return 1;
	return 0;
}
I(){
	q=E*B-F*A;
	return(C*F-D*E)*q>0&q*(A*D-B*C)>0;
}
main(v,w,o,c){
	for(;scanf("%d%d%d%d%d%d%d%d%d",&A,&B,&C,&D,&E,&F,&v,&w,&R),A;){
		A-=v,B-=w;
		C-=v,D-=w;
		E-=v,F-=w;
		o=(A*A+B*B>R*R)+(C*C+D*D>R*R)+(E*E+F*F>R*R);
		if(!o)
			puts("b");
		else if(o==3){
			c=M(C,D,E,F)|M(E,F,A,B)|M(A,B,C,D);
			if(c&2)
				puts("c");
			else if(c&1){
				if(I())
					puts("a");
				else
					puts("c");
			}else{
				if(I())
					puts("a");
				else
					puts("d");
			}
		}else
			puts("c");
	}
	return 0;
}

Compiler output:
main.c:3:1: warning: data definition has no type or storage class
    3 | A,B,C,D,E,F,R;
      | ^
main.c:3:1: error: type defaults to 'int' in declaration of 'A' [-Wimplicit-int]
main.c:3:3: error: type defaults to 'int' in declaration of 'B' [-Wimplicit-int]
    3 | A,B,C,D,E,F,R;
      |   ^
main.c:3:5: error: type defaults to 'int' in declaration of 'C' [-Wimplicit-int]
    3 | A,B,C,D,E,F,R;
      |     ^
main.c:3:7: error: type defaults to 'int' in declaration of 'D' [-Wimplicit-int]
    3 | A,B,C,D,E,F,R;
      |       ^
main.c:3:9: error: type defaults to 'int' in declaration of 'E' [-Wimplicit-int]
    3 | A,B,C,D,E,F,R;
      |         ^
main.c:3:11: error: type defaults to 'int' in declaration of 'F' [-Wimplicit-int]
    3 | A,B,C,D,E,F,R;
      |           ^
main.c:3:13: error: type defaults to 'int' in declaration of 'R' [-Wimplicit-int]
    3 | A,B,C,D,E,F,R;
      |             ^
main.c:4:1: error: return type defaults to 'int' [-Wimplicit-int]
    4 | M(a,b,c,d,e,f){
      | ^
main.c: In function 'M':
main.c:4:1: error: type of 'a' defaults to 'int' [-Wimplicit-int]
main.c:4:1: error: type of 'b' defaults to 'int' [-Wimplicit-int]
main.c:4:1: error: type of 'c' defaults to 'int' [-Wimplicit-int]
main.c:4:1: error: type of 'd' defaults to 'int' [-Wimplicit-int]
main.c:4:1: error: type of 'e' defaults to 'int' [-Wimplicit-int]
main.c:4:1: error: type of 'f' defaults to 'int' [-Wimplicit-int]
main.c:7:11: error: implicit declaration of function 'fabs' [-Wimplicit-function-declaration]
    7 |         q=fabs(-f*a+e*b)/hypot(e,f);
      |           ^~~~
main.c:1:1: note: include '<math.h>' or provide a declaration of 'fabs'
  +++ |+#include <math.h>
    1 | #define hypot _hypot
main.c:7:11: warning: incompatible implicit declaration of built-in function 'fabs' [-Wbuiltin-declaration-mismatch]
    7 |         q=fabs(-f*a+e*b)/hypot(e,f);
      |           ^~~~
main.c:7:11: note: include '<math.h>' or provide a declaration of 'fabs'
main.c:1:15: error: implicit declaration of function '_hypot'; did you mean 'hypot'? [-Wimplicit-function-declaration]
    1 | #define hypot _hypot
      |               ^~~~~~
main.c:7:26: note: in expansion of macro 'hypot'
    7 |         q=fabs(-f*a+e*b)/hypot(e,f);
      |                          ^~~~~
main.c: At top level:
main.c:15:1: error: return type defaults to 'int' [-Wimplicit-int]
   15 | I(){
      | ^
main.c:19:1: error: return type defaults to 'int' [-Wimplicit-int]
   19 | main(v,w,o,c){
      | ^~~~
main.c: In function 'main':
main.c:19:1: error: type of 'v' defaults to 'int' [-Wimplicit-int]
main.c:19:1: error: type of 'w' defaults to 'int' [-Wimplicit-int]
main.c:19:1: error: type of 'o' defaults to 'int' [-Wimplicit-int]
main.c:19:1: error: type of 'c' defaults to 'int' [-Wimplicit-int]
main.c:20:14: error: implicit declaration of function 'scanf' [-Wimplicit-function-declaration]
   20 |         for(;scanf("%d%d%d%d%d%d%d%d%d",&A,&B,&C,&D,&E,&F,&v,&w,&R),A;){
      |              ^~~~~
main.c:1:1: note: include '<stdio.h>' or provide a declaration of 'scanf'
  +++ |+#include <stdio.h>
    1 | #define hypot _hypot
main.c:20:14: warning: incompatible implicit declaration of built-in function 'scanf' [-Wbuiltin-declaration-mismatch]
   20 |         for(;scanf("%d%d%d%d%d%d%d%d%d",&A,&B,&C,&D,&E,&F,&v,&w,&R),A;){
      |              ^~~~~
main.c:20:14: note: include '<stdio.h>' or provide a declaration of 'scanf'
main.c:26:25: error: implicit declaration of function 'puts' [-Wimplicit-function-declaration]
   26 |                         puts("b");
      |                         ^~~~
main.c:26:25: note: include '<stdio.h>' or provide a declaration of 'puts'