MathNet 2019-part-01 — 184 problems (EN–VI) Question 30

Let $ABC$ be a triangle and $I$ its incenter. The circumcircle of $ACI$ intersects the line $BC$ a second time in the point $X$ and the circumcircle of $BCI$ intersects the line $AC$ a second time in the point $Y$.
Prove that the segments $AY$ and $BX$ are of equal length.