RMO 2015

Let $ABC$ be a triangle with circumcircle 􀀀 and incentre $I$ . Let the internal angle bisectors of angles $A, B$ , and $C$ meet 􀀀the circumcircle in $X, Y$ , and $Z$ respectively. Let $YZ$ intersect $AX$ in $P$ and $AC$ in $Q$ , and let $BY$ intersect $AC$ in $R$ . Suppose the quadrilateral $PIRQ$ is a kite; that is, $IP = IR$ and $QP = QR$ . The radius of the circumcircle is 2 and the area of triangle $ABC$ is expressed as $d^{3/2}$ , find the value of $\sqrt d$ .