In a non right angled triangle $\Delta PQR$, 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 $p=\sqrt{3},q=1$ and the radius of the circumcircle of the $\Delta PQR$ equals to 1, then which of the followign options is/are correct?

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