Triangle Angle Bisectors

The lines $p_{AB}$, $p_{BC}$ and $$p_{CA}$$ are the resective perpendicular bisectors of the triangle sides $AB$, $BC$ abd $CA$.
Pairwise, they intersect in 3 points. The theorem says these three points coincide as the red point I.

Patrick D. F. Ion, Created with GeoGebra