In a non-right-angled triangle $\triangle P Q R$, let $p , q , r$ denote the lengths of the sides opposite to the angles at $P , Q , R$ respectively. The median from $R$ meets the side $P Q$ at $S$, the perpendicular from $P$ meets the side $Q R$ at $E$, and $R S$ and $P E$ intersect at $O$. If $p = \sqrt { 3 } , q = 1$, and the radius of the circumcircle of the $\triangle P Q R$ equals 1, then which of the following options is/are correct? (A) Length of $R S = \frac { \sqrt { 7 } } { 2 }$ (B) Area of $\triangle S O E = \frac { \sqrt { 3 } } { 12 }$ (C) Length of $O E = \frac { 1 } { 6 }$ (D) Radius of incircle of $\triangle P Q R = \frac { \sqrt { 3 } } { 2 } ( 2 - \sqrt { 3 } )$
In a non-right-angled triangle $\triangle P Q R$, let $p , q , r$ denote the lengths of the sides opposite to the angles at $P , Q , R$ respectively. The median from $R$ meets the side $P Q$ at $S$, the perpendicular from $P$ meets the side $Q R$ at $E$, and $R S$ and $P E$ intersect at $O$. If $p = \sqrt { 3 } , q = 1$, and the radius of the circumcircle of the $\triangle P Q R$ equals 1, then which of the following options is/are correct?\\
(A) Length of $R S = \frac { \sqrt { 7 } } { 2 }$\\
(B) Area of $\triangle S O E = \frac { \sqrt { 3 } } { 12 }$\\
(C) Length of $O E = \frac { 1 } { 6 }$\\
(D) Radius of incircle of $\triangle P Q R = \frac { \sqrt { 3 } } { 2 } ( 2 - \sqrt { 3 } )$