In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, the Mandart inellipse of a triangle

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

 is the inconic having parameters
where a, b, and c are sides of the triangle

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

. It is named after H. Mandart, who studied it in two papers published in the late 19th century.

The center of the Mandart inellipse is the mittenpunkt

Mittenpunkt

In geometry, the mittenpunkt of a triangle is a triangle center: a point defined from the triangle that is invariant under Euclidean transformations of the triangle. It is defined as the symmedian point of the excentral triangle of the given triangle. It is also the centroid of the Mandart...

 of the triangle. The three lines connecting the triangle vertices to the opposite points of tangency all meet in a single point, the Nagel point

Nagel point

In geometry, the Nagel point is a point associated with any triangle. Given a triangle ABC, let TA, TB, and TC be the extouch points in which the A-excircle meets line BC, the B-excircle meets line CA, and C-excircle meets line AB, respectively...

of the triangle.