KöMaL 2020 B5091

In a regular dodecagon $A_1A_2\ldots A_{12}$, let $P$ denote the intersection of the diagonals $A_1A_8$ and $A_6A_{11}$, and let $R$ denote the intersection of lines $A_7A_8$ and $A_9A_{11}$. Show that the line $PR$ divides diagonal $A_1A_4$ in a $2:1$ ratio.