CN-TST 2022 Problem 13

Given two circles $\omega_1$ and $\omega_2$ where $\omega_2$ is inside $\omega_1$ . Show that there exists a point $P$ such that for any line $\ell$ not passing through $P$ , if $\ell$ intersects circle $\omega_1$ at $A,B$ and $\ell$ intersects circle $\omega_2$ at $C,D$ , where $A,C,D,B$ lie on $\ell$ in this order, then $\angle APC=\angle BPD$ .