Can someone help me with this geometry problem?

[jodi22]

Let I be the incenter of the triangle ABC. Suppose that the incircle touches the sides AC and AB at P and Q respectively. The lines BI and CI meet the line PQ at X and Y respectively. Prove that the points X,Y, B, C lie on a circle and determine the center of this circle.

 

[lev888]

Let I be the incenter of the triangle ABC. Suppose that the incircle touches the sides AC and AB at P and Q respectively. The lines BI and CI meet the line PQ at X and Y respectively. Prove that the points X,Y, B, C lie on a circle and determine the center of this circle.

Please post the diagram and let us know where you are stuck.