In a non right angled triangle $ΔPQR$, let $p,q,r$ denote the lengths of the sides opposite to the angle P,Q,R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. if $p=3 ,q=1$ and the radius of the circumcircle of the $ΔPQR$ equals to 1, then which of the followign options is/are correct?