Circle-inscribed Poncelet with an equilateral II: the double stationarity of X74, X110

Let T be circle-inscribed Poncelet triangles circumscribing some caustic -- let O' denote its center -- such that one of the triangles in the family is an equilateral A'B'C'. We showed in a previous video that the line X3 X74 X110 ... is stationary. An interesting question is what is the locus of O' such that the stationary axis is invariant. Mark Helman has proved the first phenomenon and also derived an interesting construction for such a locus: pick a point K on the circumcircle as the desired landing place for X110. The locus of O' is a straight line through X3 which is the reflection of the external bisector of (K X3 C') about X3 C'.

[@gregevgeni1864]

Excellent work ! 💯