excircle
nounEtymology From ex- + circle.
1
Geometry, Mathematics, Sciences 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.
- 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:
- 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:
1 more example
- 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:
- Related terms
- excenter, excentre, incircle, ex-tangential