Let $\omega$ denote the circumscribed circle of an acute-angled $\triangle ABC$ with $AB \neq BC$. Let $A'$ be the point symmetric to the point $A$ with respect to the line $BC$. The lines $AA'$ and $A'C$ intersect $\omega$ for the second time at points $D$ and $E$, respectively. Let the lines $AE$ and $BD$ intersect at point $P$. Prove that the line $A'P$ is tangent to the circumscribed circle of $\triangle A'BC$. Proposed by Oleksii Masalitin