Subject: [HM] Generalised Simson problem
From: Philippe Boulanger (philippe.boulanger@pourlascience.fr)
Date: Tue Mar 28 2000 - 03:05:38 EST
Dear sirs,
When the geometry of the triangle was taught in school, the Simson's line
was well known. And the locus of points for which the three "feet" of the
perpendiculars drawn from a point to the three sides of a triangle are
aligned on the Simson's line, is the circumscribed circle to the triangle.
Is there anything about the problem with four lines : what is the locus of
points for which the "feet" of the four perpendiculars to four lines are on
a circle? Has Simson studied the problem? Of course the locus has to go
through the six points of intersection of the four lines...
Sincerely yours,
Philippe Boulanger
philippe.boulanger@pourlascience.fr
Pour la Science
8 rue Ferou 75006
Paris
Tel : 01 55 42 84 00
http://www.pourlascience.com
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