KöMaL 2019 B5002

The graph of the cubic polynomial $x^3 +a x^2 + bx + c$ and the circle of radius $10$ centred at the origin intersect at six distinct points $P_1$, $P_2$, $P_3$, $P_4$, $P_5$, $P_6$. Express the centre of mass of the system $P_1$, $P_2$, $P_3$, $P_4$, $P_5$, $P_6$ in terms of the coefficients $a$, $b$, $c$.