HYACINTHOS 29458

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle.

Denote:

A', B', C' = the incenters of IBC, ICA, IAB, resp.

A* = (reflection of BA' in BC') /\ (reflection of CA' in CB')

B* = (reflection of CB' in CA') /\ (reflection of AB' in AC')  

C* = (reflection of AC' in AB') /\ (reflection of BC' in BA')   

A** = (reflection of BC' in BA') /\ (reflection of CB' in CA')

B** = (reflection of CA' in CB') /\ (reflection of AC' in AB')

C** = (reflection of AB' in AC') /\ (reflection of BA' in BC')

1. ABC, A*B*C* are perspective
2. ABC, A**B**C** are perspective.

Perspectors ?

APH

[Petr Moses]:

Hi Antreas,

1).
Sin[A] (1 + 2 Cos[A / 2] + 2 Cos[A]) : :
on lines: {3,1129}, {35,259}, {55,10232}

2).
Sin[A] / (1 + 2 Cos[A / 2] + 2 Cos[A])::
on lines: {}.
on {A,B,C,H,X(1127)}

1). and 2). are isogonal conjugates.

Best regards,
Peter Moses.