IMO 1987 LL FIN10

Origin: FIN

Problem

In a Cartesian coordinate system, the circle C1 has center O1(−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 \geqc min{AX, AX2}. Find the largest possible c.