- Apr 20 4:56 AM
[AH] Let D' be the point of concurrence of the above radical axes in triangle ABC and point D

and similarly C', B',A'. Which properties has the quadrangle A'B'C'D'? Are the lines AA', BB', CC', DD' concurrent?[Chris]However alas your P-NPC-Radical-Axis-Triangle Transformation doesn't produce a Quadrangle Perspector.

Neither for the 1st nor the 2nd generation.

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Dear Chris,

Thank you!So, naturally we have to return to triangle geometry and ask for locus!

That is:Let ABC be a triangle and P a point.Denote:

Ap, Bp, Cp = the isogonal conjugates of A,B,C, resp. wrt triangles

PBC, PCA, PAB, resp.

rA1 = the radical axis of NPC_ABC and NPC_ApBC

rA2 = the radical axis of NPC_APC and NPC_ApPC

rA3 = the radical axis of NPC_APB and NPC_ApPB

A' = the point of concurrence of rA1, rA2, rA3.

Similarly (cyclically) B',C'

Which is the locus of P such that ABC, A'B'C' are perspective?

Antreas