geometry

Let triangle ABC be an isosceles triangle with an incircle (I) touching sides BC, CA, and AB at points D, E, and F, respectively. Points M and N are on line segment EF such that CM is parallel to BN, which is also parallel to DA. Let the intersections of lines DM and DN with the incircle (I) be P and Q, respectively. Prove that lines BP, CQ, and AD are concurrent.