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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?

     Triangles

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.

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    $\begingroup$ Just curious: Where does this come up? $\endgroup$
    – vonbrand
    Jul 23 at 15:56
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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.

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