Dictionary

excircle en · NOUN

Pronunciation

• (US) audio

Etymology

From ex- + circle.

Meanings

1. 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.
   • 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. 1999, Art Johnson, Famous Problems and Their Mathematicians, Teacher Ideas Press, page 174:
   • Lemma 4.9 (The Diameter of the Incircle). Let ABC be a triangle whose incircle is tangent to #92;overline#123;BC#125; at D. If #92;overline#123;DE#125; is a diameter of the incircle and ray AE meets #92;overline#123;BC#125; at X, then BD#61;CX and X is the tangency point of the A-excircle to #92;overline#123;BC#125;. Incircles and excircles often have dual properties. 2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61:
   • Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself. 1979, Dan Pedoe, Circles: A Mathematical View, published 1995, page 10:

Forms

Relateds

excentre · excenter · incircle · ex-tangential

Translations (9)

ko 방접원 (escribed circle) · sv utvändig tangeringscirkel (escribed circle) · fi viereen piirretty ympyrä (escribed circle) · fi vierusympyrä (escribed circle) · vi đường tròn bàng tiếp (escribed circle) · fr cercle exinscrit (escribed circle) · ja 傍接円 (escribed circle) · pt círculo exinscrito (escribed circle) · cy allgylch (escribed circle)