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

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