#include <fstream.h>
#include <math.h>
ifstream fin("thread.dat");
//#define fin cin
const double M_PI = 3.1415926535897932384626433832795;

class Vec3D
{
public:
    double x,y,z;
    Vec3D() {};
    Vec3D(double X,double Y,double Z): x(X), y(Y), z(Z) {}
    Vec3D operator-(const Vec3D&a){return Vec3D(x-a.x,y-a.y,z-a.z);}
    double operator*(const Vec3D&a){return x*a.x+y*a.y+z*a.z;}
    void operator/=(double a){x/=a;y/=a;z/=a;}
    double module(){return sqrt(x*x+y*y+z*z);}
};

inline double sqr(double x) {return x*x;}
double distance(Vec3D &a, Vec3D &b)
{return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y)+sqr(a.z-b.z));}

void main()
{
    Vec3D a,b,c; double r;
    fin >> a.x >> a.y >> a.z;
    fin >> b.x >> b.y >> b.z;
    fin >> c.x >> c.y >> c.z;
    fin >> r;

    double da=distance(a,c), ta=sqrt(da*da-r*r);
    double db=distance(b,c), tb=sqrt(db*db-r*r);

    double alfa=asin(r/da);
    double beta=asin(r/db);
      /// alfa is angle between AC and tangent

    Vec3D ax=a-c, bx=b-c;
    ax/=ax.module(); bx/=bx.module();
    double gama=acos(ax*bx);
      // gama is angle ACB
    double delta=gama+alfa+beta-M_PI;

    cout.precision(2);
    cout << (delta<0 ? distance(a,b) : delta*r+ta+tb) << endl;
}

You should have a couple more "if"'s in your program