Let X₁, X₂, ... , X_n be n≥2 distinct points on a circle C with center O and radius r. What is the locus of points P inside C such that

   ∑ⁿ_i=1 |X_iP|/|PY_i| = n

,where the line X_iP also intersects C at point Y_i.

(In reply to Solution (spoiler) by Praneeth)

I believe the puzzle indicates the Xi and Yi are each separate points, not the coordinates of points, and therefore not numbers. |XiP| is a number only because it represents the length of line segment XiP, where P is another point (on the chord XiYi).

Posted by Charlie on 2007-12-13 10:34:15