ILL 1987 Problem 10

In a Cartesian coordinate system, the circle $C_1$ has center $O_1(-2, 0)$ and radius $3$ . Denote the point $(1, 0)$ by $A$ and the origin by $O$ .Prove that there is a constant $c > 0$ such that for every $X$ that is exterior to $C1$ , $$OX- 1 \geq c \min\{AX,AX^2\}.$$ Find the largest possible $c.$