text: #include <CGAL/Exact_circular_kernel_2.h>
  #include <CGAL/point_generators_2.h>
  #include <iostream>
  
  typedef CGAL::Exact_circular_kernel_2             Circular_k;
  
  typedef CGAL::Point_2<Circular_k>                 Point_2;
  typedef CGAL::Circle_2<Circular_k>                Circle_2;
  typedef CGAL::Circular_arc_2<Circular_k>          Circular_arc_2;
  
  template <typename T>
  double prob_2() {
    CGAL::Random_points_in_square_2<Point_2> g(1.0);
    double prob = 0.0;
    for (int i = 0; i < 10000; i++) {
  
      Point_2 p1, p2, p3, p4, p5, p6;
      p1 = *g++; p2 = *g++; p3 = *g++;
      p4 = *g++; p5 = *g++; p6 = *g++;
  
      // the pi's are points inherited from the Cartesian kernel Point_2, so,
      // the orientation predicate can be called on them
      if(CGAL::orientation(p1, p2, p3) != CGAL::COUNTERCLOCKWISE) std::swap(p1, p3);
      T o1 = T(p1, p2, p3);
      if(CGAL::orientation(p4, p5, p6) != CGAL::COUNTERCLOCKWISE) std::swap(p4, p6);
      T o2 = T(p4, p5, p6);
  
      typedef typename CGAL::CK2_Intersection_traits<Circular_k, T, T>::type
        Intersection_result;
      std::vector<Intersection_result> res;
      CGAL::intersection(o1, o2, std::back_inserter(res));
  
      prob += (res.size() != 0) ? 1.0 : 0.0;
    }
    return prob/10000.0;
  }
  
  int main()
  {
    std::cout << "What is the probability that two arcs formed by" << std::endl;
    std::cout << "three random counterclockwise-oriented points on" << std::endl;
    std::cout << "an unit square intersect? (wait a second please)" << std::endl;
    std::cout << "The probability is: " << prob_2<Circular_arc_2>() <<
      std::endl << std::endl;
  
    std::cout << "And what about the probability that two circles formed by"
      << std::endl;
    std::cout << "three random counterclockwise-oriented points on" << std::endl;
    std::cout << "an unit square intersect? (wait a second please)" << std::endl;
    std::cout << "The probability is: " << prob_2<Circle_2>() << std::endl;
    return 0;
  }
  