Language: C++

#include<bits/stdc++.h>
  
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-6)
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
  
using namespace std;
  
class Point{
public:
  double x,y;
  
  Point(double x = 0,double y = 0): x(x),y(y){}
  
  Point operator + (Point p){return Point(x+p.x,y+p.y);}
  Point operator - (Point p){return Point(x-p.x,y-p.y);}
  Point operator * (double a){return Point(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}
  Point operator * (Point a){ return Point(x * a.x - y * a.y, x * a.y + y * a.x); }
  
  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }
  
  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }
  
};
  
struct Segment{
  Point p1,p2;
  int index;
  Segment(Point p1 = Point(),Point p2 = Point(),int index=-1):p1(p1),p2(p2),index(index){}
  bool operator <  (const Segment& s) const { return ( p2 == s.p2 ) ? p1 < s.p1 : p2 < s.p2; }
  bool operator == (const Segment& s) const { return ( s.p1 == p1 && s.p2 == p2 ) || ( s.p1 == p2 && s.p2 == p1 ); }
  
};
  
typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;
  
double dot(Point a,Point b){ return a.x*b.x + a.y*b.y; }
  
double cross(Point a,Point b){ return a.x*b.y - a.y*b.x; }
  
double norm(Point a){ return a.x*a.x+a.y*a.y; }
  
double abs(Point a){ return sqrt(norm(a)); }
  
Point rotate(Point a,double rad){ return Point(cos(rad)*a.x - sin(rad)*a.y,sin(rad)*a.x + cos(rad)*a.y); }
  
double toRad(double agl){ return agl*M_PI/180.0; }
  
double getArg(Point a,Point b,Point c){
  double arg1 = atan2(b.y-a.y,b.x-a.x);
  double arg2 = atan2(c.y-b.y,c.x-b.x);
  double arg = fabs( arg1 - arg2 );
  while( arg > M_PI ) arg -= 2.0 * M_PI;
  return fabs(arg);
}
  
int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point b = p2-p0;
  if(cross(a,b) > EPS)return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS)return CLOCKWISE;
  if(dot(a,b) < -EPS)return ONLINE_BACK;
  if(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}
  
bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2-l.p1, m.p2-m.p1)) > EPS || // non-parallel
         abs(cross(l.p2-l.p1, m.p1-l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2-l.p1, s.p1-l.p1)*       // s[0] is left of l
         cross(l.p2-l.p1, s.p2-l.p1) < EPS; // s[1] is right of l
}
bool intersectLP(Line l,Point p) {
  return abs(cross(l.p2-p, l.p1-p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}
  
Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}
Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}
double distanceLP(Line l, Point p) {
  return abs(p - projection(l, p));
}
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}
  
double distanceLS(Line l, Line s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}
  
double distanceSS(Line s, Line t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}
  
Point crosspoint(Line l,Line m){
  double A = cross(l.p2-l.p1,m.p2-m.p1);
  double B = cross(l.p2-l.p1,l.p2-m.p1);
  if(abs(A) < EPS && abs(B) < EPS){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]); 
    return vec[1];
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}
  
double cross3p(Point p,Point q,Point r) { return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
    
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
    
bool ccwtest(Point p,Point q,Point r){ return cross3p(p,q,r) > 0; }
   
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}
  
// ------------------
  
Line calcLine(Line line1,Line line2,Point p1,Point p2){
  Point cp = crosspoint(line1,line2);
  double S = heron(p1,cp,p2);
  double a = abs(p1-cp);
  double b = abs(p2-cp);
  double arg_a = asin((2.0*S)/(a*b));
  if( equals(2*S,a*b) ) arg_a = toRad(90);

  int res = ccw(cp,p1,p2);

  Point base;
  if( res == COUNTER_CLOCKWISE ) base = p1;
  else                           base = p2;
  Point not_base = (base==p1)?p2:p1;
  arg_a = (toRad(180.0)-getArg(base,cp,not_base));

  Vector e = ( base - cp ) / abs( base - cp );
  e = rotate(e,arg_a/2.0);
  Line tmp = Line(cp,cp+e*100);
  return tmp;
}
  
const string MANY = "Many";
const string NONE = "None";
void compute(vector<Line> &vec){
  
  if( vec.size() <= 2 ) { cout << MANY << endl; return; }
  
  vector<Line> candidateLines;
  int n = vec.size();
  rep(i,n) REP(j,i+1,n){
    if( equals(cross(vec[i].p1-vec[i].p2,vec[j].p1-vec[j].p2),0.0) ) {
      Vector e = ( vec[i].p2 - vec[i].p1 ) / abs( vec[i].p2 - vec[i].p1 );
      e = rotate(e,toRad(90));
      Line line = Line(vec[i].p1,vec[i].p1+e*100);
      Point cp1 = crosspoint(line,vec[i]);
      Point cp2 = crosspoint(line,vec[j]);
      Point mp = ( cp1 + cp2 ) / 2.0;
      e = ( vec[i].p2 - vec[i].p1 ) / abs( vec[i].p2 - vec[i].p1 );
      line = Line(mp,mp+e*100);
      line.index = candidateLines.size();
      candidateLines.push_back(line);
    } else {
      Point cp = crosspoint(vec[i],vec[j]);
      Point I = ( vec[i].p1 == cp ) ? vec[i].p2 : vec[i].p1;
      Point J = ( vec[j].p1 == cp ) ? vec[j].p2 : vec[j].p1;
      Vector e1 = ( I - cp ) / abs( I - cp );
      Vector e2 = ( J - cp ) / abs( J - cp );
      Line tmp = calcLine(vec[i],vec[j],cp+e1*100,cp+e2*100);
      int Index = candidateLines.size();
      tmp.index = Index;
      candidateLines.push_back(tmp);
      tmp = calcLine(vec[i],vec[j],cp+e1*100,cp-e2*100);
      tmp.index = Index;
      candidateLines.push_back(tmp);
    }
    if( candidateLines.size() >= 30 ) break;
  }
    
  vector<Point> candidatePoints;
  
  rep(i,candidateLines.size()) REP(j,i+1,candidateLines.size()) {
    Line line1 = candidateLines[i];
    Line line2 = candidateLines[j];
    if( equals(cross(line1.p1-line1.p2,line2.p1-line2.p2),0.0) ) continue;
    Point cp = crosspoint(line1,line2);    
    candidatePoints.push_back(cp);
  }
  
  vector<Point> &v = candidatePoints;
  sort(v.begin(),v.end());
  v.erase(unique(v.begin(),v.end()),v.end());
  
  vector<Point> answer;
  rep(i,candidatePoints.size()){
    Point p = candidatePoints[i];
    double dist = -1;
    bool success = true;
    rep(j,vec.size()){
      double tmp = distanceLP(vec[j],p);
      if( equals(dist,-1) ) dist = tmp;
      else if( !equals(dist,tmp) ) { success = false; /*break;*/ }
    }
    if( success ) answer.push_back(p);
    if( answer.size() >= 2 ) break;
  }
  
  if( answer.size() == 1 ) printf("%.10f %.10f\n",answer[0].x,answer[0].y);
  else if( answer.empty() ) cout << NONE << endl;
  else cout << MANY << endl;
}
  
int main(){
  int n;
  while( cin >> n, n ){  
    vector<Line> vec(n);
    rep(i,n) cin >> vec[i].p1.x >> vec[i].p1.y >> vec[i].p2.x >> vec[i].p2.y;
    compute(vec);
  }
  return 0;
}

Compiler output:
a.cc: In function 'Line calcLine(Line, Line, Point, Point)':
a.cc:153:14: error: 'heron' was not declared in this scope
  153 |   double S = heron(p1,cp,p2);
      |              ^~~~~