HYACINTHOS 8072

Dear friends,

I cite Kimberling's ETC (with slight modification):

Let A', B', C' be the first points of intersection
of the angle bisectors of triangle ABC with its
incircle. The tangents at A', B', C' to the
incircle form a triangle A"B"C" called the
"tangential mid-arc triangle" of ABC.

Now, triangle A"B"C" is perspective to the intouch
triangle of triangle ABC at a point with trilinears

( (cos B/2 + cos C/2 - cos A/2) sec A/2 : ... ).

It is not in ETC. It lies on the line (1, 167, 174,
177, 503). We can call it "3rd Mid-arc point" of
triangle ABC.

Sincerely,
Darij Grinberg