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 Locus of Points (Posted on 2007-12-12)
Let X1, X2, ... , Xn 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

∑ni=1 |XiP|/|PYi| = n

,where the line XiP also intersects C at point Yi.

 See The Solution Submitted by Bractals Rating: 3.0000 (2 votes)

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 re: Solution | Comment 15 of 16 |
(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 2007-12-14 12:52:55

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