About planar $(\alpha,\beta)$–accessible domains

The article is devoted to the class $A^{\alpha,\beta}_{\rho}$ of all $(\alpha,\beta)$–accessible with respect to the origin domains $D,$ $\alpha,\beta\in[0,1),$ possessing the property\thinspace $\rho=\min\limits_{p\in\partial D}|p|,$\thinspace where\thinspace $\rho\thinspace\in \thinspace(0,+\infty)$ is a fixed number. We find the maximal set of points $a$ such that all domains $D\in A^{\alpha,\beta}_{\rho}$ are $(\gamma,\delta)$–accessible with respect to $a,$ $\gamma\in[0;\alpha],$ $\delta\in[0;\beta]$. This set is proved to be the closed disc of center $0$ and radius $\rho\sin\displaystyle\frac{\varphi\pi}{2},$ where $\varphi=\min\left\{\alpha-\gamma,\beta-\delta\right\}$.