# RMO 2015

**Geometry**Level 4

Let \(ABC\) be a triangle with circumcircle τ and incentre \(I\). Let the internal angle bisectors of angles \(A, B\), and \(C\) meet τthe 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 \(\sqrt d\).

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