Tactics : Black to Play...carefully

I know that if this was in a blitz game, there would be a very high chance of me failing to play this correctly.

I think its a great problem, where a solution jumps out at you, but when you calculate it, you see the lurking issue that stops your idea and have to re-think.

Well, at least I did. 

My re-appraisal found a better solution, then I had to go through it again as, in my mind, I saw the king on the 'wrong' square, so that solution didn't work either. Except it did, when I adjusted my vision !

Its probably simpler for you...

Black to play

Tactic :White to Play

A holiday, and other less pleasant distractions, kept me on a low run-rate with Chess Tempo, and has driven my RD ( Rating deviation ) up, meaning that failures cost a lot of rating points !

However, a recent dedicated run of 20+ problems in a single session has put me back on track, gaining few points with it, but some interesting positions.

I suspect tiredness played its part in taking far too long on the below.

The point of the problem was whether White could take the hanging Rook on a3.

There is no White mate ( Ng8 will stop it ) and the passed pawn cannot win the Rook via any Queen sacrifice, but I could not get past the fact that after 1. Qxa3 Qc1+ and Black would regain the Rook.

Maybe in a real game I wouldn't have looked for longer, but knowing that ChessTempo only views +1.75 pawns as a correct solution, eventually, it clicked...

White to play

Enjoy, and here's the solution.