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# Inellipse

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 (Dörrie 1965, p. 217).

The area of an inellipse with center having areal coordinates inscribed in a triangle is

 (1)

where is the area of the reference triangle (Chakerian 1979, pp. 143 and 148), which corresponds to an inellipse with center having exact trilinear coordinates having area

 (2) (3)

In terms of the inconic parameters , the formula is even simpler,

 (4)

(E. W. Weisstein, Dec. 4, 2005).

The following table summarizes the areas of some special inellipses.

The centers of the ellipses inscribed in a quadrilateral all lie on the straight line segment joining the midpoints of the polygon diagonals (Chakerian 1979, pp. 136-139).

Brocard Inellipse, Circumellipse, Hofstadter Ellipse, Incircle, Lemoine Inellipse, Mandart Inellipse, MacBeath Inconic, Orthic Inconic, Steiner Inellipse

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## References

Chakerian, G. D. "A Distorted View of Geometry." Ch. 7 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., 1979.Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, 1965.

Inellipse

## Cite this as:

Weisstein, Eric W. "Inellipse." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Inellipse.html