bool solve()
{
int N;
std::scanf("%d", &N);
if(N == 0) return false;
for(int i = 0; i != N; ++i)
std::scanf("%lf %lf", &pt[i].x, &pt[i].y);
std::random_shuffle(pt, pt + N);
point_t c = pt[0];
double r = 0.0;
for(int i = 1; i != N; ++i)
{
if(dist(pt[i], c) <= r + eps)
continue;
c = pt[i], r = 0.0;
for(int j = 0; j != i; ++j)
{
if(dist(pt[j], c) <= r + eps)
continue;
c = middle_point(pt[i], pt[j]);
r = dist(c, pt[i]);
for(int k = 0; k != j; ++k)
{
if(dist(pt[k], c) <= r + eps)
continue;
c = incenter(pt[i], pt[j], pt[k]);
r = dist(c, pt[i]);
}
}
}
std::printf("%.2lf %.2lf %.2lf\n", c.x, c.y, std::sqrt(r));
return true;
}
/* create a biarc for a bezier curve.
*
* extends the tangent lines to the bezier curve at its first and last control
* points, and intersects them to find a third point.
* the biarc passes through the first and last control points, and the incenter
* of the circle defined by the first, last and intersection points.
*/
HIDDEN ON_Arc
make_biarc(const ON_BezierCurve& bezier)
{
ON_2dPoint isect, arc_pt;
ON_2dPoint p_start(bezier.PointAt(0)), p_end(bezier.PointAt(1.0));
ON_2dVector t_start(bezier.TangentAt(0)), t_end(bezier.TangentAt(1.0));
ON_Ray r_start(p_start, t_start), r_end(p_end, t_end);
r_start.IntersectRay(r_end, isect);
arc_pt = incenter(p_start, p_end, isect);
return ON_Arc(p_start, arc_pt, p_end);
}
