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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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 three points again | Comment 6 of 16 |

The following two diagrams illustrate the symmetry of X1 and X2 separated by 90 degrees, and then a distortion when X3 is introduced off-axis. By aligning the axis vertically, the stretching/compression doesn't affect the symmetry/asymmetry.

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*****************************************************************************     &nbs

Posted by Charlie
on 2007-12-13 00:18:04

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