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 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_{i}P/PX_{i} = n
Note the numerator and denominator interchanged making each term in the sum the reciprocal.

Posted by Charlie
on 20071215 18:13:44 