Παρασκευή, 9 Δεκεμβρίου 2011

NINE POINT CIRCLE


Let ABC be a triangle, A'B'C' the orthic triangle and P a point.


Let A*,B*,C* be the orthogonal projections of A,B,C on the line OP, resp.
Let L1,L2,L3 be the reflections of A'A*,B'B*,C'C* in the altitudes AA',BB',CC', resp. and M1,M2,M3 the parallels through A,B,C, to L1,L2,L3, resp.

The lines M1,M2,M3 concur at a point Q on the Nine Point Circle of ABC (Q is the center of the rectangular circumhyperbola which is the isogonal conjugate of the line OP)

APH, 9 December 2011

1 σχόλιο:

  1. I have posted a solution to this problem here:-
    http://www.artofproblemsolving.com/Forum/viewtopic.php?f=46&t=331763&&start=1111
    See post no. 1112 and 1114

    ΑπάντησηΔιαγραφή

 

Free Hit Counter