HYACINTHOS 28116

Antreas Hatzipolakis

 

 

Let ABC be a triangle and A'B'C' the pedal triangle of O.

Denote:

Ab, Ac = the orthogonal projections of A' on AB, AC, resp.

Bc, Ba = the orthogonal projections of B' on BC, BA, resp.  

Ca, Cb = the orthogonal projections of C' on CA, CB, resp.  

 

(Oa), (Ob), (Oc) = the circles with diameters AbAc, BcBa, CaCb, resp.

R1, R2, R3 = the radical axes of ((Ob),(Oc)), ((Oc),(Oa)), ((Oa),(Ob)), resp.

 

The reflections of R1, R2, R3 in BC, CA, AB, resp. concur at a point on the Euler line of ABC.

APH