Newton-Gauss line

by henderson, Jun 1, 2016, 6:35 PM

Among the points $A, B, C, D$ no three are collinear. The lines $AB$ and $CD$ intersect at $E,$ and $BC$ and $DA$ intersect at $F.$ Prove that either the circles with diameters $AC, BD, EF$ pass through a common point, or no two of them have any common point.

$\blacktriangleright$ The line through the midpoints of $AC, BD, EF$ is called the $\bf\color{red}Newton-Gauss \ line. \ $
This post has been edited 1 time. Last edited by henderson, Jun 1, 2016, 6:36 PM

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This is the Gauss Bodenmiller theorem. http://mathworld.wolfram.com/Gauss-BodenmillerTheorem.html

by brainjam, Jun 26, 2018, 2:29 AM

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complex bash :)

by bever209, Jul 10, 2020, 4:04 PM

"Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater." - Albert Einstein

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