HYACINTHOS 26201

[Antreas P. Hatzipolakis]

 

Let ABC be a triangle and P a point.

Denote:

A', B', C' = the reflections of A, B, C in P, resp.

Ab, Ac = the orthogonal projections of A' on BP, CP, resp.

Na = the NPC center of A'AbAc, Similarly Nb, Nc.

Which is the locus of P such that ABC, NaNbNc are

1. perspective?
I lies on the locus. Perspector?

2. orthologic?


[Peter Moses]:

Hi Antreas

 

1). Among others, Q030.

 

X(1) ->  (a^2-7 a b+b^2-c^2) (a^2-b^2-7 a c+c^2):: = Sin[A]/(7-2 Cos[A]):: 

on lines {{1, 3530}, {8, 4540}, {21, 3635}, {79, 9957}, {80, 5919},...}.

on Feuerbach.

isoconjugate of X(58) and X(3968).

barycentric quotient X(37)/X(3968).

 

X(4) -> a^2 (a^4-2 a^2 b^2+b^4+7 a^2 c^2+7 b^2 c^2-8 c^4) (a^4+7 a^2 b^2-8 b^4-2 a^2 c^2+7 b^2 c^2+c^4):: 

on lines {{3,5888},{6,11455},{54, 12112},{67,10721},...}.

6 X[3]-7 X[5888].

on Jerabek.

isogonal conjugate of X(8703).

X(54)-vertex conjugate of X(3431).

 

 

Best regards,

Peter Moses.