Originally posted by Artardo
Just off the top of my head, rather than 37.Ra7+ I'd try something like 37.c4, with the plan being to block the k-side pawn majority and letting black figure out how to stop the 3 passed pawns. For example, 37...dxc4 38.Ke3 f5 39.g3 intending a4.
I agree, Ra7+ is it. His rook and king can't really move, because your g pawn is invincible (because of Ra7+ threat) and if the rook moves it queens. So you can just improve your position with moves like g3, Ke2. The c4 move is really nice, I wouldn't have seen it right away and I'm pretty sure it's best.
Anyways, the most important thing is, ''The threat is stronger than the execution''. In your case the threat of Ra7+ (protecting the pawn) was much more important than playing Ra7+ right away