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)
As an example, consider the circle x˛+y˛=1, with two given points: X1 = (1,0), and X2 = (1,0), both lying on the circle.
If the locus sought in this case is a circular arc, what are you claiming is the center and radius of that circular arc? I'll assume that your claim is that all parts of such a defined circle that lie within the given circle constitute the arc that is the locus; otherwise specify what portion of the newly defined circle is the arc in question.
Edited on December 14, 2007, 12:54 pm

Posted by Charlie
on 20071214 12:52:55 