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[[File:Mandart inellipse - resized.svg|thumb|300px|Mandart inellipse (red), touching the triangle (black) in contact points of excircles (gray). In green, lines identifying Nagel point (N) and, in blue, lines identifying mittenpunkt (M).]]
In [[geometry]], the '''Mandart inellipse''' of a [[triangle]] is an [[ellipse]] inscribed within the triangle, tangent to its sides at the contact points of its [[excircle]]s (which are also the vertices of the [[extouch triangle]]).<ref>{{citation
| last = Juhász | first = Imre
| journal = Annales Mathematicae et Informaticae
| mr = 3005114
| pages = 37–46
| title = Control point based representation of inellipses of triangles
| url = http://ami.ektf.hu/uploads/papers/finalpdf/AMI_40_from37to46.pdf
| volume = 40
| year = 2012}}.</ref> The Mandard inellipse is named after H. Mandart, who studied it in two papers published in the late 19th century.<ref name="g04">{{citation|last=Gibert|first=Bernard|title=Generalized Mandart conics|journal=Forum Geometricorum|url=http://forumgeom.fau.edu/FG2004volume4/FG200421.pdf|year=2004|volume=4|pages=177–198}}.</ref><ref>{{citation|last=Mandart|first=H.|title=Sur l’hyperbole de Feuerbach|journal=[[Mathesis (journal)|Mathesis]]|year=1893|pages=81–89}};
{{citation|last=Mandart|first=H.|title=Sur une ellipse associée au triangle|journal=[[Mathesis (journal)|Mathesis]]|year=1894|pages=241–245|url=http://books.google.com/books?id=kqAKAAAAYAAJ&pg=PA241}}. As cited by {{harvtxt|Gibert|2004}}.</ref>
 
==Parameters==
As an [[inconic]], the Mandart inellipse is described by the [[parameters]]
:<math>x:y:z=\frac{a}{b+c-a}:\frac{b}{a+c-b}:\frac{c}{a+b-c}</math>
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.<ref name="g04"/>
 
==Notes==
{{Reflist}}
 
==External links==
*{{mathworld|urlname=MandartInellipse|title=Mandart Inellipse}}
 
[[Category:Triangle geometry]]

Latest revision as of 01:40, 10 September 2013

Mandart inellipse (red), touching the triangle (black) in contact points of excircles (gray). In green, lines identifying Nagel point (N) and, in blue, lines identifying mittenpunkt (M).

In geometry, the Mandart inellipse of a triangle is an ellipse inscribed within the triangle, tangent to its sides at the contact points of its excircles (which are also the vertices of the extouch triangle).[1] The Mandard inellipse is named after H. Mandart, who studied it in two papers published in the late 19th century.[2][3]

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.[2]

Notes

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    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

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    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

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    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

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