MathNet 2013 Question 4

Let two circles ω₁,ω₂ intersect at X,Y. A circle ω is internally tangent to ω₁ and ω₂ at P and Q respectively. Segment XY meets ω at M,N. Rays PM and PN meet ω₁ at A,D; rays QM and QN meet ω₂ at B,C. Prove AB=CD.