Let $\Omega$ be a circle, and let $A$, $B$, $C$, $D$ and $K$ be distinct points on it, in that order, and such that lines $BC$ and $AD$ are parallel. Let $A'\neq A$ be a point on line $AK$ such that $BA=BA'$. Similarly, let $C'\neq C$ be a point on line $CK$ such that $DC=DC'$. Prove that segments $AC$ and $A'C'$ have the same length.