BALKAN-SL 2021 G7

Let $A B C$ be an acute scalene triangle. Its $C$-excircle tangent to the segment $A B$ meets $A B$ at point $M$ and the extension of $B C$ beyond $B$ at point $N$. Analogously, its $B$-excircle tangent to the segment $A C$ meets $A C$ at point $P$ and the extension of $B C$ beyond $C$ at point $Q$. Denote by $A_{1}$ the intersection point of the lines $M N$ and $P Q$, and let $A_{2}$ be defined as the point, symmetric to $A$ with respect to $A_{1}$. Define the points $B_{2}$ and $C_{2}$, analogously. Prove that $\triangle A B C$ is similar to $\triangle A_{2} B_{2} C_{2}$.