The billiard circumellipse, also called the circumbilliard, of a noncollinear triangle 
is the unique circumellipse
in which 
is a closed billiard trajectory. Its center
is the mittenpunkt 
(Reznik and Garcia 2021, p. 33). It is the orthic
inconic of the excentral triangle and touches
its sides at 
, 
, and 
(Reznik and Garcia 2021, p. 45).
The billiard circumellipse and the Mandart inellipse are confocal ellipses (Reznik and Garcia 2021, p. 49). By Poncelet's porism, infinitely many triangles are inscribed in the billiard circumellipse and circumscribed about the Mandart inellipse. They are all closed billiard trajectories and have the same maximal perimeter among triangles inscribed in the billiard circumellipse (Nieuw Archief voor Wiskunde, Theorem 1.1). For an equilateral triangle, the billiard circumellipse is the circumcircle and the two foci coincide.
