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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 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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and also | Comment 8 of 16 |

Although the puzzle specifies n to be at least 2, when n is 1 there's also a locus that meets the criteria. It's just a circle half the diameter of circle C, with one of its diameters on C and the other at O. The points of the locus are the midpoints of all chords with one end at the given X1. Perhaps this was considered too trivial to be considered to be within the scope of the puzzle.


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     -                                                          ***********************        -    
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      -                                                             ***************           -     
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  Posted by Charlie on 2007-12-13 00:21:20
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