>> It's the point of intersection of lines through the
>> midpoints of a triangle perpendicular to the opposite sides
>> of the orthic triangle.

Well... This is the center of the nine-point circle!

Where have you found the definition?

Perhaps, the "Kantor point" was asked for?

My apologies if I am replying to a discussion settled over a year ago...

Friendly,
Darij Grinberg

So it is.
>
>Where have you found the definition?

Check this:

https://www.cut-the-knot.org/Curriculum/Geometry/CantorPoint.shtml

The reference is to Honsberger's Chestnuts.

>Perhaps, the "Kantor point" was asked for?

Nope. The history of this is that long ago I wrote an applet (available at https://www.cut-the-knot.org/triangle/tri.shtml where it had to be popped up) with some remarkable points, lines and circles in a triangle. I did not give a second thought to the terminology. With a hindsight I probably should not have done that. The question that started this thread refers to Cantor point in that applet. At the time the question was asked the point was not mentioned anywhere else. Thus in parallel with answering the question I added a page which I have mentioned above. The theorem is Cantor's. Whether a well known point deserves an additional name is a different matter. Honestly, I am not sure about that, but adding to the site is easier than modifying it and it is more entertaining. So I let it be, at least for the time being.

All the best,
Alex

Many thanks for the information. I see Cantor proved a generalization of the nine-point center to polygons; hence, there is a good reason to name the point for Cantor. In Germany, the nine-point center is usually called "Feuerbachpunkt" ("Feuerbach point"), what has the great disadvantage to conflict with the majority of other countries, where the "Feuerbach point" is the point of tangency of the nine-point circle with the incircle. It is really better to speak of a nine-point center and a Feuerbach tangency point.

Sincerely,
Darij Grinberg