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[Aomandeyi <>]

Aha! i can give you counter-example:
------------------------------
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <sstream>
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::Point_2 Point_2;
int main()
{
        Point_2 p(0, 0.4), q(1, 0.7), r(2, 1);
        {
                std::cout << std::setprecision(17) << p << " " << q << " " << 
r << "\n";
                std::cout << (CGAL::collinear(p, q, r) ? "collinear\n" : "not
collinear\n");
        }
        
        {
                q = CGAL::midpoint(p, r);
                std::cout << std::setprecision(17) << p << " " << q << " " << 
r << "\n";
                std::cout << (CGAL::collinear(p, q, r) ? "collinear\n" : "not
collinear\n");
        }
        

        return 0;
}
--------------------
the results:the same input but different output
----------------------------------------
0 0.40000000000000002 1 0.69999999999999996 2 1
not collinear
0 0.40000000000000002 1 0.69999999999999996 2 1
collinear
---------------------------------------------



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