The tangential mid-arc triangle of a reference triangle Δ A B C is the triangle Δ A' B' C' whose sides are the tangents to the incircle at the intersections of the internal angle bisectors with the incircle, where the points of intersection nearest the vertices are chosen. It has trilinear vertex matrix [-y x | z(z + x) | y(y + x) z(z + y) | -z x | x(x + y) y(y + z) | x(x + z) | -x y, ] where x = cos(A/2), y = cos(B/2), and z = cos(C/2).

angle bisector | circumcircle mid-arc triangle | incircle | mid-arc triangle | tangential mid-arc circle