The triangle Δ A' B' C' formed by the points of pairwise intersection of the three intangents. It is not in perspective with Δ A B C. It has trilinear vertex matrix [1 + cos A | cos A - cos C | cos A - cos B cos B - cos C | 1 + cos B | cos B - cos A cos C - cos B | cos C - cos A | 1 + cos C], or [a(b + c - a) | (c - a)(c + a - b) | (b - a)(b + a - c) (c - b)(c + b - a) | b(c + a - b) | (a - b)(a + b - c) (b - c)(b + c - a) | (a - c)(a + c - b) | c(a + b - c)] (Kimberling 1998, p. 161).

extangents triangle | intangent | intangents circle