Language: C++

#include <cstdio>
#include <iostream>
#include <complex>

using namespace std;

#define dump(n) cerr<<"# "<<#n<<"="<<(n)<<endl

const double EPS=1e-9;
const double INFTY=1e12;
typedef complex<double> Point;

struct Line{
	Point pos,dir;
	Line(){}
	Line(Point p,Point d):pos(p),dir(d){}
};

int Signum(double x)
{
	return abs(x)<EPS?0:x>0?1:-1;
}

double Dot(Point a,Point b)
{
	return real(conj(a)*b);
}

double Cross(Point a,Point b)
{
	return imag(conj(a)*b);
}

int CCW(Point a,Point b,Point c)
{
	Point d1=b-a,d2=c-a;
	int sign=Signum(Cross(d1,d2));
	
	if(sign)
		return sign;	// 1:ccw,-1:cw
	if(Dot(d1,d2)<-EPS)
		return -2;		// c-a-b
	if(norm(d1)<norm(d2)-EPS)
		return 2;		// a-b-c
	return 0;			// a-c-b
}

// ツ点ツづ陳シツ静シツづ個仰猟猟」
double DistancePL(Point p,Line l)
{
	return abs(Cross(p-l.pos,l.dir))/abs(l.dir);
}
// ツ点ツづ静シツ閉ェツづ個仰猟猟」
double DistancePS(Point p,Line s)
{
	Point a=p-s.pos,b=s.dir;
	Point c=b*Dot(a,b)/norm(b);
	double pos=abs(c)/abs(b);
	if(-EPS<pos && pos<1+EPS)
		return abs(a-c);
	else
		return min(abs(a),abs(b-a));
}

void solve(Point p[],Point c,int r)
{
	{	// triangle in circle
		double dist=0;
		for(int i=0;i<3;i++)
			dist=max(dist,norm(p[i]-c));
		if(dist<=r*r){
			puts("b");
			return;
		}
	}
	
	{	// circle in triangle
		bool res=true;
		int ccw=0;
		for(int i=0;i<3;i++){
			int temp=CCW(p[i],p[(i+1)%3],c);
			if(abs(temp)==2)
				continue;
			res&=temp*ccw>=0;
			ccw=temp;
		}
		if(res){
			double dist=INFTY;
			for(int i=0;i<3;i++)
				dist=min(dist,DistancePL(c,Line(p[i],p[(i+1)%3]-p[i])));
			if(Signum(dist-r)>=0){
				puts("a");
				return;
			}
		}
	}
	
	{	// intersect
		double dist=INFTY;
		for(int i=0;i<3;i++)
			dist=min(dist,DistancePS(c,Line(p[i],p[(i+1)%3]-p[i])));
		if(Signum(dist-r)<=0){
			puts("c");
			return;
		}
	}
	
	puts("d");
}

int main()
{
	for(;;){
		Point p[3],c;
		double r;
		for(int i=0;i<3;i++)
			cin>>real(p[i])>>imag(p[i]);
		cin>>real(c)>>imag(c)>>r;
		if(norm(p[0])==0)
			break;
		
		//for(int i=0;i<3;i++)
		//	printf("(%.3f,%.3f) ",real(p[i]),imag(p[i]));
		//printf("(%.3f,%.3f,%.3f)\n",real(c),imag(c),r);
		
		solve(p,c,r);
	}
	
	return 0;
}

Compiler output:
a.cc: In function 'int main()':
a.cc:117:28: error: no match for 'operator>>' (operand types are 'std::istream' {aka 'std::basic_istream<char>'} and 'double')
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                         ~~~^~~~~~~~~~~~
      |                         |        |
      |                         |        double
      |                         std::istream {aka std::basic_istream<char>}
In file included from /usr/include/c++/14/iostream:42,
                 from a.cc:2:
/usr/include/c++/14/istream:170:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(bool&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  170 |       operator>>(bool& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:170:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'bool&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:174:7: note: candidate: 'std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(short int&) [with _CharT = char; _Traits = std::char_traits<char>]' (near match)
  174 |       operator>>(short& __n);
      |       ^~~~~~~~
/usr/include/c++/14/istream:174:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'short int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:177:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(short unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  177 |       operator>>(unsigned short& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:177:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'short unsigned int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:181:7: note: candidate: 'std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(int&) [with _CharT = char; _Traits = std::char_traits<char>]' (near match)
  181 |       operator>>(int& __n);
      |       ^~~~~~~~
/usr/include/c++/14/istream:181:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:184:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  184 |       operator>>(unsigned int& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:184:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'unsigned int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:188:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  188 |       operator>>(long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:188:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'long int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:192:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  192 |       operator>>(unsigned long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:192:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'long unsigned int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:199:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  199 |       operator>>(long long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:199:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'long long int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:203:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  203 |       operator>>(unsigned long long& __n)
      |       ^~~~~~~~
/usr/include/c++/14/istream:203:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'long long unsigned int&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:219:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(float&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  219 |       operator>>(float& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:219:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'float&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:223:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  223 |       operator>>(double& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:223:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'double&' to an rvalue of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:227:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long double&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]' (near match)
  227 |       operator>>(long double& __f)
      |       ^~~~~~~~
/usr/include/c++/14/istream:227:7: note:   conversion of argument 1 would be ill-formed:
a.cc:117:34: error: cannot bind non-const lvalue reference of type 'long double&' to a value of type 'double'
  117 |                         cin>>real(p[i])>>imag(p[i]);
      |                              ~~~~^~~~~~
/usr/include/c++/14/istream:328:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(void*&) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]'
  328 |       operator>>(void*& __p)
      |       ^~~~~~~~
/usr/include/c++/14/istream:328:25: note:   no known conversion for argument 1 from 'double' to 'void*&'
  328 |       operator>>(void*& __p)
      |                  ~~~~~~~^~~
/usr/include/c++/14/istream:122:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(__istream_type& (*)(__istream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>]'
  122 |       operator>>(__istream_type& (*__pf)(__istream_type&))
      |       ^~~~~~~~
/usr/include/c++/14/istream:122:36: note:   no known conversion for argument 1 from 'double' to 'std::basic_istream<char>::__istream_type& (*)(std::basic_istream<char>::__istream_type&)' {aka 'std::basic_istream<char>& (*)(std::basic_istream<char>&)'}
  122 |       operator>>(__istream_type& (*__pf)(__istream_type&))
      |                  ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/istream:126:7: note: candidate: 'std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(__ios_type& (*)(__ios_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __istream_type = std::basic_istream<char>; __ios_type = std::basic_ios<char>]'
  126 |       operator>>(__ios_type& (*__pf)(__ios_type&))
      |       ^~~~~~~~
/usr/include/c++/14/istream:126:32: note:   no known conversion for argument 1 from 'double' to 'std::basic_istream<char>::__ios_type& (*)(std::basic_istream<char>::__ios_type&)' {aka 'std::basic_ios<char>& (*)(std::basic_ios<char>&)'}
  126 |       operator>>(__ios_type& (*__pf)(__ios_type&))
      |                  ~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~
/usr/