Problem

Source: Tuymaada 2024 Senior league P6

Tags: geometry



The triangle $ABC$ is given. On the arc $BC$ of its circumscribed circle, which does not contain point $A$, the variable point $X$ is selected, and on the rays $XB$ and $XC$, the variable points $Y$ and $Z$, respectively, so that $XA = XY = XZ$. Prove that the line $YZ$ passes through a fixed point. Proposed by A. Kuznetsov