Let X
_{1}, X
_{2}, ... , 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
_{i}P/PY
_{i} = n
,where the line X
_{i}P 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 20071213 10:34:15 