HYACINTHOS 21045

Dear friends:

The incircle and Steiner inellipse intersect in 4 points, one of which, say P, is a triangle center, and the other 3, say A', B', C', form a central triangle (similar to the intersections of NPC and Steiner inellipse = X(115) + medial triangle). P is a non-ETC center, search=2.307963780976356, and A'B'C' is perspective to ABC at non-ETC center, say X, search=1.626790309962831.

Questions:

1.) What are the coordinates of P, A', B', C', and X?

2.) For the ETC reference triangle, A' is the farthest of the 4 intersections from A, and likewise for B' and C'. Does this hold in general?

3.) For the ETC reference triangle, P is the closest of the 4 intersections to X(11). Does this hold in general?

4.) Any other interesting properties?

5.) Generalizations for other inconics?

Thanks in advance,
Randy Hutson