new definition of Kiepert axes?
- Wilson, François, Jean-Pierre, Bernard, Peter, and all,
In checking Wilson's statements last night I noticed that there is a
point on each axis of the Steiner ellipses where the its tripolar and
its dual are perpendicular. The dual of course is always
perpendicular to an axis, so at these points these lines are parallel
to the Steiner axes. They seem to go through the Kiepert center mS
(the medial Steiner point). Hence there seems to be a point on each
axis whose dual and tripolar line form the axes of the Kiepert
hyperbola. By intermediate values the points have to exist. That
these lines are the Kiepert axes is conjecture.
It will be easy to find these points but I am occupied by my conics
writeups so it will wait. I suspect the the existence of the points
is more interesting than the points themselves.
Triangle web page: