Como construir (obter) o ponto D ?

A figura encontra-se no anexo (arquivo jpg).

Espero que ele a mostre.




[Attachment(s) from Antreas Hatzipolakis included below]

Nguyen Minh Tuan? wrote in a FB group (*):

Let ABC be a triangle and D a point such that the circles inscribed in the 
triangles ABD, BCD, and CAD pairwise touch each other. On lines BC, CA, AB, AD, 
BD, CD, denote the touching points by A1, B1, C1, A2, B2, C2, resp. Let lines 
B1C2 and B2C1 meet at E and let lines A1C2 and A2C1 meet at F . Show that the 
lines AF , BE and C1D are concurrent.


Let's replace E = B1C2 intersection B2C1 with Cb and F = A1C2 intersection A2C1 
with Ca.
Let C* be the point of concurrence of ACa , BCb and C1D.
Similarly A* and B*.

Are the triangles ABC, A*B*C* perspective?




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