Κυριακή 20 Οκτωβρίου 2019

HYACINTHOS 16676

 
 
Dear Hyacinthists,
 
let ABC be a triangle, O the circumcenter, I the incenter, A' the midpoint of BC, Fe the Feuerbach's point, P the intersection of OI and  BC, and P' the foot of the perpendicular on AO issue from P. 
Result1 :    Fe, A' and P' are collinear.
Let La be the line PP' and cyclically Lb, Lc
A* the point of intersection of Lb ans Lc and cyclically B*, C*.
Result 2 : the triangles ABC and A*B*C* are perspective.
Question : is the perspector in ETC?

Sincerely
Jean-Louis Ayme

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