Noun
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.
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Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself.
More examples (2)
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.
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.