KöMaL 2021 C1659

Ray $a$ starts from point $A$ of a line segment $AB$, and encloses an angle $0^\circ<\alpha<90^{\circ}$ with it. Ray $b$ starts from point $B$, and encloses an angle $0^\circ<\beta<90^{\circ}$ with the line segment $AB$. The two rays lie in two different half planes of a plane containing line $AB$. The circle of diameter $AB$ intersects $a$ again at $A_1$, and $b$ at $B_1$. The circle of diameter $A_1B_1$ intersects the line containing $a$ again at $A_2$, and the line containing $b$ at $B_2$. What is the relationship between $\alpha$ and $\beta$ if $A_1B_1$ and $A_2B_2$ are perpendicular?