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Locus of Points (Posted on 2007-12-12) Difficulty: 4 of 5
Let X1, X2, ... , Xn be n≥2 distinct points on a circleC 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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution Comment 16 of 16 |
(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

ni=1 |YiP|/|PXi| = 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
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