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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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third point | Comment 3 of 16 |

Adding a third point (X3) off the axis of symmetry results in a disjoint locus, with the smaller piece seeming to pull a section of the larger piece toward it, making the larger piece asymmetrical. Remember again, the locus is the boundary of the *'d area, not the interior. The Xn's are at 0, 80 and 200 degrees, which are then points of tangency except that the actual point of tangency in each case is missing from the locus due to the lack of definition of the ratio of lengths there.

 

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                                      ---                   ---                                     
                                           ------- -------                                          

  Posted by Charlie on 2007-12-12 22:04:34
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