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 by Praneeth)

Praneeth is absolutely correct, though I still do not understand the derivation. Also, the circular arc seems to be a full circle, rather than just an arc.

What I had explored was a slightly different puzzle, where

‡”ⁿ_i=1 |Y_iP|/|PX_i| = n

Note the numerator and denominator interchanged making each term in the sum the reciprocal.

Posted by Charlie on 2007-12-15 18:13:44