ZA-SAMO 2020 Problem 5

Let $ABC$ be a triangle, and let $T$ be a point on the extension of $AB$ beyond $B$ , and $U$ a point on the extension of $AC$ beyond $C$ , such that $BT = CU$ . Moreover, let $R$ and $S$ be points on the extensions of $AB$ and $AC$ beyond $A$ such that $AS = AT$ and $AR = AU$ . Prove that $R$ , $S$ , $T$ , $U$ lie on a circle whose centre lies on the circumcircle of $ABC$ .