Παρασκευή 17 Μαΐου 2013

CONCURRENT CIRCUMCIRCLES - CONCYCLIC POINTS

Let ABC be a triangle, Na,Nb,Nc the NPC centers of IBC, ICA, IAB, resp. and Oa, Ob, Oc the circumcenters of NaBC, NbCA, NcAB, resp.

1. The Euler line of NaNbNc is the line INF of ABC (O of NaNbNc = N of ABC, H of NaNbNc = I of ABC, F of ABC = ?? of NaNbNc).

2. The circumcircles (Oa),(Ob),(Oc) of NaBC, NbCA, NcAB, resp. concur at a point Q on the circumcircle of NaNbNc.

Which point is the Q wrt 1. ABC 2.NaNbNc ?

Antreas P. Hatzipolakis, 17 May 2013

-

Δεν υπάρχουν σχόλια:

Δημοσίευση σχολίου

Εγγραφή σε: Σχόλια ανάρτησης (Atom)

FOUR POINTS ON THE EULER LINE

Problem by Antreas Hatzipolakis Solution by Francisco Javier García Capitán FOUR POINTS ON THE EULER LINE ETC LISTINGS X(726...

  • EUCLID 4404
  • ETC
    X(5459) Let ABC be a triangle, let A', B', C' be the midpoints of BC, CA, AB. Let L_a be the perpendicular through A' ...
  • HOMOTHETIC TRIANGLES and EULER LINES
    Theorem 1. Let ABC be an equilateral triangle and P a point. The Euler lines of the triangles PBC,PCA,PAB are concurent.Denote the point ...