excircle

Definitions

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.

Equivalents

Examples

“Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself.”

“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.”

CEFR level