The radius of an excircle. Let a triangle have exradius r_A (sometimes denoted ρ_A), opposite side of length a and angle A, area Δ, and semiperimeter s. Then r_1 | = | Δ/(s - a) | = | sqrt((s(s - b)(s - c))/(s - a)) | = | 4R sin(1/2 A) cos(1/2 B) cos(1/2 C) (Johnson 1929, p. 189), where R is the circumradius.

circle | circumradius | excircles | inradius | radius