HYACINTHOS 5321

Antreas P. Hatzipolakis

 

Let ABC be a triangle and A'B'C' the intouch triangle of ABC
(= the pedal triangle of I).

The perp. from C' to BC intersects again the incircle in C'a
The perp. from B' to BC intersects again the incircle in B'a


A
/\
/ \
/ \
/ \
C' B'
/ A0 \
/ C'a B'a \
B------A1------C

A0 := BC'a /\ CB'a. Similarly B0,C0

A1 := Orth. Proj. of A0 on BC. Similarly B1,C1.

The Triangles:

1. ABC, A0B0C0

2. ABC, A1B1C1

are perspective.

Perspectors in Normals:

1. (1-cosA)/cos^2A ::) = (sin^2(A/2)/cos^2A ::)

2. (1-cosA)/(1+cosA)cosA ::) = (tan^2(A/2)/cosA ::)


Antreas