Question 28
Let $\triangle ABC$ be a regular triangle. Point $T$ is chosen on its side $AC$, and points $M$ and $N$ are chosen respectively on arcs $AB$ and $BC$ of its circumcircle so that $MT \parallel BC$ and $NT \parallel AB$. Segments $AN$ and $MT$ intersect at $X$, while segments $CM$ and $NT$ intersect at $Y$. Prove that the polygons $AXYC$ and $XMBNY$ have equal perimeters. (V. Shmarov)