Mathematics - Circle Question with Solution | TestHub

Let $C_1:x^2+y^2=1;C_2:(x-10{)}^2+y^2=1$ and $C_3:x^2+y^2-10x-42y+457=0$ be three circles. A circle $C$ has been drawn to touch circles $C_1$ and $C_2$ externally and $C_3$ internally. Now circles $C_1$, $C_2$ and $C_3$ start rolling on the circumference of circle $C$ in anticlockwise direction with constant speed. The centroid of the triangle formed by joining the centres of rolling circles $C_1,C_2$ and $C_3$ lies on