MathNet 2022-part-01 — 197 problems (EN–VI) Question 66

Let $ABC$ be an isosceles triangle with the base $BC$. Points $X$, $Y$ and $Z$ are chosen on the sides $BC$, $AC$ and $AB$, respectively, such that $\triangle ABC \sim \triangle YXZ$. Let $W$ be the reflection of $X$ with respect to the midpoint of the segment $BC$.
Prove that the points $X$, $Y$, $Z$ and $W$ are cocyclic.