different between excentre vs excircle

English

Noun

excentre (plural excentres)

1. (Britain) Alternative spelling of excenter

Anagrams

• excenter, exercent

French

Pronunciation

• Homophones: excentrent, excentres

Verb

excentre

1. first-person singular present indicative of excentrer
2. third-person singular present indicative of excentrer
3. first-person singular present subjunctive of excentrer
4. third-person singular present subjunctive of excentrer
5. second-person singular imperative of excentrer

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