P0 = the orthopole of PO wrt ABC
P1 = the orthopole of PQ1 wrt QBC
P2 = the orthopole of PQ2 wrt QCA
P3 = the orthopole of PQ3 wrt QAB
1. P0, P1, P2, P3 lie on the NPCs (N),(N1),(N2),(N3) of ABC, QBC, QCA, QAB, resp. (since the respective lines pass through the circumcenters of the respective triangles)
2. The NPCs of ABC, QBC, QCA, QAB concur at the Poncelet point Q* of Q wrt ABC.
The points P0, P1, P2, P3, Q* are concyclic.
Antreas P. Hatzipolakis, 30 March 2013.