2022 IMO Problems/Problem 4

Problem 4. Let ABCDE be a convex pentagon such that BC = DE. Assume that there is a point T inside ABCDE with TB = TD, TC = TE and ∠ABT = ∠TEA. Let line AB intersect lines CD and CT at points P and Q, respectively. Assume that the points P, B, A, Q occur on their line in that order. Let line AE intersect lines CD and DT at points R and S, respectively. Assume that the points R, E, A, S occur on their line in that order. Prove that the points P, S, Q, R lie on a circle.