A triangle inscribed in (ABC)

We study a problem proposed by José Manuel Sánchez Muñoz in the Telegram group Retos Matemáticos. The proposed gives a point Pa on the circumcircle of a triangle, then we find a triangle formed by the points corresponding to the three vertices.

The triangle PaPbPc happens to be perspective with all the circumcevians triangles of points on the trilinear polar of a specific line, namely the trilinear polar of the Gergonne point.

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