Question 22
Let $ABCD$ be a tangential quadrilateral whose inscribed circle touches the sides $AB$, $BC$, $CD$ and $DA$ in points $P$, $Q$, $R$ and $S$, respectively. Let the lines $AB$ and $CD$ intersect at a point $E$, and let the lines $AD$ and $BC$ intersect at a point $F$. Denote $I_1$ the intersection point of the bisectors of the angles $\angle QPS$ and $\angle PSR$, and denote $I_2$ the intersection point of the bisectors of the angles $\angle RQP$ and $\angle SRQ$. Prove that the lines $AC$, $EF$ and $I_1I_2$ either intersect at a common point or are parallel.