Question 126
A point $S$ lies on the side $PM$ of a trapezoid $MPQ$ with bases $PM$ and $RQ$ ($PQ \lt PM$, and $S$ is distinct from the vertices). The bisectors of the angles $MSQ$ and $MPQ$ meet at point $O$. It is known that the segment $OI$, where $I$ is the incenter of the triangle $PQR$, is parallel to the bases of the trapezoid. Prove that $SR = OI$.