A circle with huge equation

 Antreas Hatzipolakis proposes the problem Euclid 3637 as follows:

Let ABC be a triangle, L the Euler line, P a point on L and A'B'C' the pedal triangle of P
Denote
A", B", C" = the orthogonal projections of A, B, C, on L, resp.
(Oa), (Ob), (Oc) = the circles with diameters A'A", B'B", C'C", resp.
The radical center of (Oa), (Ob), (Oc) lies on the NPC.
Which point is it in terms of P?

Here is the Mathematica code and its output to the solution of this problem and its generalization for any line $px + qy + rz =0$.

Solution to Euclid Problem 3637