# RMO 2015

Geometry Level 4

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 $$\sqrt d$$.

×