22. Since the quadrilateral $O A_{1} B B_{1}$ is cyclic, $\angle O A_{1} B_{1}=\angle O B C$. By using the analogous equalities we obtain $\angle O A_{4} B_{4}=\angle O B_{3} C_{3}=\angle O C_{2} D_{2}=$ $\angle O D_{1} A_{1}=\angle O A B$, and similarly $\angle O B_{4} A_{4}=\angle O B A$. Hence $\triangle O A_{4} B_{4} \sim$ $\triangle O A B$. Analogously, we have for the other three pairs of triangles $\triangle O B_{4} C_{4} \sim \triangle O B C, \triangle O C_{4} D_{4} \sim \triangle O C D, \triangle O D_{4} A_{4} \sim \triangle O D A$, and consequently $A B C D \sim A_{4} B_{4} C_{4} D_{4}$.