different between excenter vs excircle

English

Etymology

ex- +? center

Noun

excenter (plural excenters)

1. (US, geometry) The center of an excircle.

Translations

See also

• excircle

Anagrams

• excentre, exercent

English

Etymology

ex- +? circle

Noun

excircle (plural excircles)

1. (geometry) An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the lines on which the sides of the polygon lie.
   • 1979, Dan Pedoe, Circles: A Mathematical View, 1995, page 10,

     Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself.

   • 1999, Art Johnson, Famous Problems and Their Mathematicians, Teacher Ideas Press, page 174,

     Extend the sides of triangle QRS and construct the three excircles: One excircle is tangent to side QR and rays SQ and SR; one excircle is tangent to side SR and rays QS and QR; and one excircle is tangent to side SQ and rays RS and RQ.

   • Incircles and excircles often have dual properties.

Usage notes

Any given triangle has exactly three excircles. A quadrilateral that has an excircle is said to be ex-tangential (or sometimes exscriptible).

Related terms

• excentre / excenter
• incircle

Translations

See also

• ex-tangential