HATZIPOLAKIS - SUPPA CIRCLE

Locus Problem:

Let ABC be a triangle, A'B'C' the pedal triangle of H and P a point.
Denote: (Oa), (Ob), (Oc) = the circumcircles of (AA'A"), (BB'B|), (CC'C") resp. (ie the circles with diameters AA", BB", CC", resp)

(O'a), (O'b), (O'c) = the reflections of (Oa), (Ob), (Oc) in AA', BB'. CC', resp.

R'a = the radical axis of (O'b), (O'c)
R'b = the radical axis of (O'c), (O'a)
R'c = the radical axis of (O'a), (O'b)

R'1, R'2, R'3 = the reflections of R'a, R'b, R'c in BC, CA, AB, resp.
The locus of P such that the parallels to R'1, R'2, R'3 through A',B',C', resp. is the circle (X(382), R), the reflection of the circumcircle in the orthocenter H.

The circle is named HATZIPOLAKIS - SUPPA circle

Let Q5=Q5(P) be the concurrency point.

*** ETC points on the circle:
X(i), i=10152,10721,10722,10723,10724,10725,10726,10727,10728,10729,10730,10731,10732,10733,10734,10735,10736,10737,14989

*** ETC pairs (P=X(i),Q5=X(j)): {10152,133},{10721,125},{10722,115},{10723,114},{10724,119},{10725,118},{10726,124},{10727,116},{10728,11},{10729,5511},{10730,5510},{10731,25640},{10732,117},{10733,113},{10734,5512},{10735,132},{10736,1312},{10737,1313},{14989,3258}

*** Q5(P)=image of P under the homotety with center H and factor k=-1/2
*** The locus of points Q5(P) with P∈(X(382),R) is the ninepoint circle of ABC.

Reference: Euclid 2592