Some (new ?) general perspectors
- Dear Hyacinthians,
consider a triangle ABC, its intouch triangle A'B'C'
and a point P inside ABC.
Let A* be the intersection nearest to A of AP and the incircle.
Define B* and C* similarly.
Let Ab be the second intersection of A*B and the incircle.
Define Ac, Bc, Ba, Ca and Cb similarly.
The lines CaCb, BcBa and AbAc form a triangle A0B0C0.
The lines AbBa, BcCb and CaAc form a triangle A1B1C1.
The lines BaCa, CbAb and AcBc form a triangle A2B2C2.
1) A0B0C0 and ABC are perspective
2) A1B1C1 and ABC are perspective
3) A2B2C2 and A'B'C' are perspective
4) A0B0C0, A1B1C1 and A2B2C2 are perspective
Of course the incircle can be replaced by any inconic
Greetings from Bruges