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There exist a constant c

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September 5, 2010
analytic geometrygeometry unsolvedgeometry

Problem Statement

In a Cartesian coordinate system, the circle C1C_1 has center O1(−2,0)O_1(-2, 0) and radius 33. Denote the point (1,0)(1, 0) by AA and the origin by OO.Prove that there is a constant c>0c > 0 such that for every XX that is exterior to C1C1, OX−1≥cmin⁡{AX,AX2}.OX- 1 \geq c \min\{AX,AX^2\}. Find the largest possible c.c.
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