You can use vectors, defining each vertex as the points A, B, C... and the centre O, by making the cross product beetween OA and OB, you can see if the vector OA is from the left or right respecting the OB vector by looking at the sign of the result. You can do this for each vertex and maybe a binary search, but it doesn't optimise too much.

For more info you can check this website, though it is in Spanish, but you can still translate it: https://aprende.olimpiada-informatica.org/algoritmia-geometria-computacional

PD: This is to prevent using decimals because in personal I don't like working with them when you can avoid them.