In a non-right-angled triangle $$\triangle PQR$$,let p, g,r denote the lengths of the sides opposite to the angles at P,Q,R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at FE, and RS and PE intersect at O. If $$p = \sqrt 3, q = 1,$$ and the radius of the circumcircle of the $$\triangle PQR$$ equals 1, then which of the following options is/are correct?