The anticomplementary triangle is the triangle Δ A_1^, A_2^, A_3^, which has a given triangle Δ A_1 A_2 A_3 as its medial triangle. It is therefore the anticevian triangle with respect to the triangle centroid G, and is in perspective with Δ A B C at G. It is the polar triangle of the Steiner circumellipse. Its trilinear vertex matrix is [-a^(-1) | b^(-1) | c^(-1) a^(-1) | -b^(-1) | c^(-1) a^(-1) | b^(-1) | -c^(-1)] or [-b c | a c | a b b c | -c a | b a c b | c a | -a b].

anticevian triangle | anticomplementary circle | exmedian | exmedian point | Johnson circles | medial triangle | triangle centroid