Does this triangle have a name?

Question

For any triangle $A$ (black below), form an enclosing triangle $B$ with sides perpendicular to $A$'s angle bisectors (red). Does this triangle $B$ (blue) have a name?

     

A nod to vonbrand's question: This came up in exploring geodesics on a tetrahedron. It would take me far afield to explain more fully.

Answer 1

We could possibly call it the Anticevian triangle with respect to the incenter,

Edit: Using the above and google it seems it is called the Excentral triangle.