// Choose some good generator of randomness for the shuffle

mt19937_64 gen(...);

mec enclosing_circle(vector<point> &p) {

int n = p.size();

ranges::shuffle(p, gen);

auto C = mec{p[0], p[1]};

for(int i = 0; i < n; i++) {

In a[cyclic quadrilateral](https://en.wikipedia.org/wiki/Cyclic_quadrilateral), if $c$ and $z$ are from the same side of $ab$, then the angles are equal, and willad up to $0^\circ$ when summed up signed (i.e. positive if counter-clockwise and negative if clockwise). Correspondingly, if $c$ and $z$ are on the opposite sides, the angles will add up to $180^\circ$.

In a[cyclic quadrilateral](https://en.wikipedia.org/wiki/Cyclic_quadrilateral), if $c$ and $z$ are from the same side of $ab$, then the angles are equal, and willadd up to $0^\circ$ when summed up signed (i.e. positive if counter-clockwise and negative if clockwise). Correspondingly, if $c$ and $z$ are on the opposite sides, the angles will add up to $180^\circ$.

<center>

<img src="https://upload.wikimedia.org/wikipedia/commons/3/30/Opposing_inscribed_angles.svg">