Some here may be interested in the update of p. 4 of my Homepage at
https:/mysite.mweb.co.za/residents/profmd/homepage4.html with an
article of mine on a generalization of the Spieker circle & the Nagel
line (contains links to Sketchpad sketches), as well as a cartoon and
quote on mathematics. (Refresh browser window if necessary).Though I thought the above results were original when I first discovered
these, if I recall correctly, they all appear in Wilson Stothers'
website at:
https://www.maths.gla.ac.uk/~wws/cabripages/triangle/ninepoint/ninepoin
t.htm
and/or are among Bernard Gibert's work at:
https://perso.wanadoo.fr/bernard.gibert/files/bicevian.html
My homepage also includes a not so well-known generalization of the nine-point circle to a conic, and an associated generalization of the Euler line.
Among others, it also includes articles on variations of Viviani, and generalizations of Van Aubel's theorem, the Fermat-Torricelli point, etc.
Regards
Michael
Michael de Villiers
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