The angles QBP and QPA are equal by the alternate segment theorem for the larger circle. The angles QPA and AQC are equal by the alternate segment theorem for the smaller circle, where C is on the line BQ on the opposite side of Q from B.

Therefore the angles QBP and CQA are equal, which makes the lines AQ and BP parallel.

[You can find the statement and proof of the alternate segment theorem here. Scroll down towards the bottom of the page.]