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incenter (Definition)

The incenter of a geometrical shape is the center of the incircle (if it has any). The radius of the incircle is sometimes called the inradius.

On a triangle the incenter always exists and it is the intersection point of the three internal angle bisectors. So in the next picture, $AX,BY,CZ$ are angle bisectors, and $AB,BC,CA$ are tangent to the circle.

\includegraphics{incentre}




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"incenter" is owned by mps. [ full author list (3) | owner history (2) ]
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See Also: incircle, lengths of angle bisectors, angle bisector as locus, orthocenter, triangle, Ceva's theorem, Lemoine point, Gergonne point, Gergonne triangle, trigonometric version of Ceva's theorem

Other names:  incentre
Also defines:  inradius

Attachments:
proof of triangle incenter (Proof) by rm50
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Cross-references: circle, tangent, angle bisectors, point, intersection, triangle, radius, incircle, center
There are 8 references to this entry.

This is version 7 of incenter, born on 2002-01-08, modified 2008-09-30.
Object id is 1451, canonical name is Incenter.
Accessed 14306 times total.

Classification:
AMS MSC51M99 (Geometry :: Real and complex geometry :: Miscellaneous)

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