The circum-medial triangle Δ A' B' C' is the circumcevian triangle of a reference triangle Δ A B C with respect to the triangle centroid G of Δ A B C. It has trilinear vertex matrix [-a b c | c(b^2 + c^2) | b(b^2 + c^2) c(c^2 + a^2) | -a b c | a(c^2 + a^2) b(a^2 + b^2) | a(a^2 + b^2) | -a b c]. Its area is Δ' = ((a^2 + b^2 + c^2)^3 Δ)/([2(a^2 + b^2) - c^2][2(a^2 + c^2) - b^2][2(b^2 + c^2) - a^2]), where Δ is the area of Δ A B C.

circumcevian triangle | medial triangle