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

Denote:

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

A2, A3 = the reflections of A in Ab, Ac, resp.

Simpler definition of A2, A3:

The circle (A', A'A) intersects AC at A2 and AB at A3

(Oa) = the circumcircle of AA2A3 [Oa = A']

Na = the NPC center of AA2A3

Similarly (Ob), (Oc) and Nb,Nc.

1. Denote:

Ra = the radical axis of (Ob) and (Oc), Similarly Rb.Rc.

[concurrent at the radical center of the circles]

The parallels to Ra,Rb,Rc through A,B,C, resp. are concurrent (??)

2. Denote:

Sa = the radical axis of (Nb) and (Nc), Similarly Sb,Sc.

[concurrent at the radical center of the circles]

The parallels to Sa,Sb,Sc though A',B',C', resp. are concurrent (??)