incircle

English

The incircle of a triangle

Etymology

in- +‎ circle

Noun

incircle (plural incircles)

1. (geometry) A circle within a polygon, especially a triangle, that is tangent to each side.
   • 2003, Clark Kimberling, Geometry in Action: A Discovery Approach Using the Geometer's Sketchpad, page 16:

     To construct the incircle of ΔABC, we need the center of the circle and a pass-through point.

   • 2005, István Reiman, International Mathematical Olympiad: 1959-1975, page 51:

     Having constructed K, the incircle of the quadrilateral can be easily constructed since it is tangent to BA and BC.

   • 2012, Tom M. Apostol, Mamikon A. Mnatsakanian, New Horizons in Geometry, Mathematical Association of America, page 106:

     For example, in Figure 4.2a only two edges of the polygon are tangent to the incircle. The other four edges do not even touch the incircle, but their extensions, shown by dotted lines, are tangent to the incircle.

Usage notes

A triangle always has an incircle, whose centre (the incentre) is the point of concurrence of the angle bisectors. A polygon that has an incircle is called a circumscribed polygon or tangential polygon and is said to be inscribable.

Synonyms

• (circle tangent to all sides): inscribed circle

Related terms

• incentre / incenter
• inradius
• insphere

Translations

the circle within a polygon that is tangent to each side

• Bulgarian: вписана окръжност f (vpisana okrǎžnost)
• Chinese:

  Cantonese: 內接圓／内接圆 (noi⁶ zip³ jyun⁴), 內切圓／内切圆 (noi⁶ cit³ jyun⁴)

  Mandarin: 內接圓／内接圆 (zh) (nèijiēyuán), 內切圓／内切圆 (zh) (nèiqiēyuán)

• Finnish: sisään piirretty ympyrä, sisäympyrä
• French: cercle inscrit m
• German: Inkreis (de) m
• Greek: εγγεγραμμένος κύκλος (el) m (engegramménos kýklos)
• Hungarian: beírt kör (hu)
• Japanese: 内接円 (ja) (naisetsuen)
• Korean: 내접원 (ko) (naejeobwon)
• Portuguese: círculo inscrito m
• Swedish: invändig tangeringscirkel c
• Vietnamese: đường tròn nội tiếp

Verb

incircle (third-person singular simple present incircles, present participle incircling, simple past and past participle incircled)

1. Archaic form of encircle.

See also

• excircle
• circumcircle

Anagrams

• circline