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. Let r be the inradius, then 4R = r_1 + r_2 + r_3 - r 1/r_1 + 1/r_2 + 1/r_3 = 1/r (Casey 1888, p.

circle | circumradius | excircles | inradius | radius