Let ABC be a triangle, P a point and A'B'C' the 1. cevian 2. the pedal

triangle of P.

Denote:

Ab = (Parallel to AB through B') /\ BC

Ac = (Parallel to AC through C') /\ BC

Aa = (Parallel to AB through B') /\ (Parallel to AC through C')

Similarly:

Bc = (Parallel to BC through C') /\ CA

Ba = (Parallel to BA through A') /\ CA

Bb = (Parallel to BC through C') /\ (Parallel to BA through A')

Ca = (Parallel to CA through A') /\ AB

Cb = (Parallel to CB through B') /\ AB

Cc = (Parallel to CA through A') /\ (Parallel to CB through B')

A* = AbBb /\ AcCc, B* = BcCc /\ BaAa, C* = CaAa /\ CbBb

Which is the locus of P such that:

1. ABC, A*B*C*

2. A'B'C', A*B*C*

are perspective?

Variations:

A* = AbCc /\ AcBb, B* = BcAa /\ BaCc, C* = CaBb /\ CbAa

Antreas