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?
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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