Let T=ABC be a triangle family interscribed between two circles K=(O,1) and K'=(I,r), with r given by Chapple's formula. Loci of its triangle centers is studied in [1]. Let T'=A'B'C' be the projected image of T under some fixed projectivity M. The video explores invariants of the loci of X2,X3,X4 of T' as I is slid horizontally between O and the extreme right of K. Namely, it looks like for any fixed M, and over all I on that line, the loci of X2 and X4 conserve both orientation and eccentricity, with the loci of X3 conserving neither.

geogebra: https://www.geogebra.org/classic/m7xe...

[1] Boris Odehnal, "Poristic Loci of Triangle Centers", Journal for Geometry and Graphics, Volume 15 (2011), No. 1, 45–67.