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 re(2): Solution (spoiler) by Praneeth)

If (xi,yi) are the coordinates of Xi, what are the coordinates of Yi?

What is meant by XiP also intersects C at point Yi?

Posted by Charlie on 2007-12-14 00:47:20