excircle
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English[edit]
Noun[edit]
excircle (plural excircles)
 (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.
 2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads^{[1]}, page 61:
 Lemma 4.9 (The Diameter of the Incircle). Let be a triangle whose incircle is tangent to at . If is a diameter of the incircle and ray meets at , then and is the tangency point of the excircle to .
 Incircles and excircles often have dual properties.
 1979, Dan Pedoe, Circles: A Mathematical View, 1995, page 10,
Usage notes[edit]
Any given triangle has exactly three excircles. A quadrilateral that has an excircle is said to be extangential (or sometimes exscriptible).
Related terms[edit]
Translations[edit]
escribed circle

