HYACINTHOS 8088

Dear friends,
Let A1,B1,C1 be the second intersections of AI,BI,CI
with three excircles.
Then
1.Ttriangles A1B1C1 and medial triangle of triangle ABC
are perspective at point
P1(sin(B/2)+sin(C/2):sin(C/2)+sin(A/2):sin(A/2)+sin(B/2))
2.Triangles A1B1C1 and intouch triangle of triangle ABC
are perspective at point
P2([1/(s-a)]*[sin(B/2)+sin(C/2)]*sin(A/2):
[1/(s-b)]*[sin(C/2)+sin(A/2)]*sin(B/2):
[1/(s-c)]*[sin(A/2)+sin(B/2)]*sin(C/2)).
The coordinate are barycentric.
P1,X(174) and G are collinear.
As I could check these points are not in ETC.

Best regards
Milorad R.Stevanovic