A, B, C in BC, CA, AB, respectively. Then the perspectrix

(axis of perspective) of triangles ABC and A'B'C' is the

tripolar of the nine-point center of triangle ABC.

If X, Y, Z are the reflections of the incenter I of ABC

in BC, CA, AB, respectively, then the perspectrix of

triangles ABC and A'B'C' is the tripolar of X(226) of

triangle ABC.

I wonder if these properties are known.

Darij Grinberg