Locus Invariants of Projected Circle-Inscribed Triangle Families VII: over all nested caustics

Let T=ABC be a circle inscribed triangle family and K' be its caustic. Let T'=A'B'C' be the image of T under M, a 3x3 projectivity. The video shows that the loci of X2 and X4 of T' conserve both orientation and eccentricity over all K'.