An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to inscribing an ellipse in a convex quadrilateral.

Brocard inellipse | circumellipse | Hofstadter ellipse | incircle | Lemoine inellipse | MacBeath inconic | Mandart inellipse | orthic inconic | Steiner inellipse