MathNet 2019-part-01 — 184 problems (EN–VI) Question 160

The point $C$ with an abscissa $-2$ lies on the hyperbola $y = 1/x$. Two lines with slopes $2$ and $1/2$ pass through $C$ and intersect the hyperbola for the second time at the points $A$ and $B$.
Find the coordinates of the circumcenter of the triangle $ABC$.