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In geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the Mandart inellipse of a triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
is an ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
that is inscribed within the triangle, tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points o ...
to its sides at the contact points of its excircles (which are also the vertices of the extouch triangle and the endpoints of the splitters). The Mandart inellipse is named after H. Mandart, who studied it in two papers published in the late 19th century..;
. As cited by .
Parameters
As an inconic, the Mandart inellipse is described by the parameters : where ''a'', ''b'', and ''c'' are sides of the given triangle.Related points
The center of the Mandart inellipse is the mittenpunkt 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 of the triangle.See also
* Steiner inellipse, a different ellipse tangent to a triangle at the midpoints of its sidesNotes
External links
*{{mathworld, urlname=MandartInellipse, title=Mandart Inellipse Curves defined for a triangle