excircle
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English
[edit]Etymology
[edit]Pronunciation
[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, published 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.
Usage notes
[edit]Any given triangle has exactly three excircles. A quadrilateral that has an excircle is said to be ex-tangential (or sometimes exscriptible).
Related terms
[edit]Translations
[edit]escribed circle
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