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Example of an inellipse
In triangle geometry, an inellipse is an ellipse that touches the three sides of a triangle. The simplest example is the incircle. Further important inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and Brocard inellipse (see examples section). For any triangle there exist an infinite number of inellipses.
The Steiner inellipse plays a special role: Its area is the greatest of all inellipses.
Because a non-degenerate conic section is uniquely determined by five items out of the sets of vertices and tangents, in a triangle whose three sides are given as tangents one can specify only the points of contact on two sides. The third point of contact is then uniquely determined.
inellipses are the Steiner inellipse, which touches the triangle at the midpoints of its sides, the Mandart inellipse and Brocard inellipse (see examples section)...
In geometry, the Steiner inellipse, midpoint inellipse, or midpoint ellipse of a triangle is the unique ellipse inscribed in the triangle and tangent...
In geometry, the Mandart inellipse of a triangle is an ellipse that is inscribed within the triangle, tangent to its sides at the contact points of its...
{\displaystyle c} remains constant. Every triangle has a unique Steiner inellipse – an ellipse inside the triangle and tangent to the midpoints of the three...
triangle, the inellipse with its center at that point is unique.: p.142 The inellipse with the largest area is the Steiner inellipse, also called the...
also called the Steiner circumellipse to distinguish it from the Steiner inellipse, is the unique circumellipse (ellipse that touches the triangle at its...
(non-Euclidean geometry) Hypotenuse Incircle and excircles of a triangle Inellipse Integer triangle Isodynamic point Isogonal conjugate Isoperimetric point...
triangle and tangent to all three sides. Every triangle has a unique Steiner inellipse which is interior to the triangle and tangent at the midpoints of the...
triangle. Every triangle has an inscribed ellipse, called its Steiner inellipse, that is internally tangent to the triangle at the midpoints of all its...
the centroid, inellipses: ellipses which touch the sides of a triangle. Special cases are the Steiner inellipse and the Mandart inellipse. Ellipses appear...
the Gergonne point. The mittenpunkt is also the centroid of the Mandart inellipse of the given triangle, the ellipse tangent to the triangle at its extouch...
the roots of the derivative of the cubic are the foci of the Steiner inellipse of the triangle—the unique ellipse that is tangent to the triangle at...
inscribed ellipses. One of them is a circle, and one of them is the Steiner inellipse which is tangent to the triangle at the midpoints of the sides. Every...
the feet of the altitudes),: p. 19 and the only triangle whose Steiner inellipse is a circle (specifically, the incircle). The triangle of largest area...
S2CID 12307207. Scimemi, Benedetto, "Simple Relations Regarding the Steiner Inellipse of a Triangle", Forum Geometricorum 10, 2010: 55–77. An interactive applet...
Power of a point – Relative distance of a point from a circle Steiner inellipse – Unique ellipse tangent to all 3 midpoints of a given triangle's sides...
also made by August Leopold Crelle and Carl Gustav Jacob Jacobi. Mandart inellipse Trisected perimeter point Dussau, Xavier. "Elementary construction of...
orthic inconic that is tangent to the sides of the triangle △ABC is an inellipse and the orthic inconics of the other three possible triangles are hyperbolas...
233, Lemma 1 A point in the interior of a triangle is the center of an inellipse of the triangle if and only if the point lies in the interior of the medial...
point. This is shown in blue and labelled "N" in the diagram. The Mandart inellipse is tangent to the sides of the reference triangle at the three vertices...
excircles of a triangle, as well as the triangle's inconics that are not inellipses, are externally tangent to one side and to the other two extended sides...
normed space made into a compact metric space. Ellipsoid method Steiner inellipse, the special case of the inner Löwner–John ellipsoid for a triangle. Fat...
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