- Apr 19 7:03 PMAntreasAre the lines AA', BB', CC', DD' concurrent?Which properties has the quadrangle A'B'C'D'?and similarly C', B',A'.Let D' be the point of concurrence of the above radical axes in triangle ABC and point DWe can apply this to a quadrangle ABCD to get another quadrangle.I quote my message #21938 to Hyacinthos:As it was proved the locus is indeed the whole plane.

Let ABC be a triangle, P, P* two isogonal conjugate points.

Denote:

Ra = radical axis of (NPC_PBC), (NPC_P*BC)

Rb = radical axis of (NPC_PCA), (NPC_P*CA)

Rc = radical axis of (NPC_PAB), (NPC_P*AB)

Which is the locus of P such that Ra,Rb,Rc are concurrent?

The entire plane?

[NPC_PBC means the Nine Point Circle of the triangle PBC]

https://groups.yahoo.com/neo/groups/Hyacinthos/conversations/messages/21938