Problem 4 Let ABC be an acute triangle with incentre I and AB≠AC. Let lines BI and CI intersect the circumcircle of ABC at P≠B and Q≠C, respectively. Consider points R and S such that AQRB and ACSP are parallelograms (with AQ ∥ RB, AB ∥ QR, AC ∥ SP , and AP ∥ CS). Let T be the point of intersection of lines RB and SC. Prove that points R, S, T , and I are concyclic.