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.

It is a combination of st. line(point is outside the circle)
and a circular arc (otherwise).
St. line:
x(Σxi) + y(Σyi) = nr²
Circular arc:
x²+y²-2x(Σxi)/(n+1)-2y(Σyi)/(n+1)=0.

Assumption: Equation of given circle is x²+y²=r².

Edited on December 13, 2007, 3:32 am

Posted by Praneeth on 2007-12-13 01:44:59