HYACINTHOS 22995

Antreas P. Hatzipolakis

 

 

Let ABC be a triangle, A'B'C' the pedal triangle of a point P

A"B"C" the pedal triangle of the circumcenter O' of A'B'C',

A*B*C* the antipodal triangle of A'B'C' (ie A*,B*,C* = the
antipodes of A',B',C') and Ma, Mb, Mc the midpoints of

A"A*, B"B*, C"C*, resp.

The circumcenter Q of MaMbMc lies on the line PO'

Which is the ratio QO' / QP ?

For P = O, (O' = N):  is Q (on the Euler line) listed in ETC?

APH