1...Qg2+ and black wins.

1.Rh7+ Qxh7 2.Qxc1#

Much better.

It's a nice puzzle in my way...

queen can't do g2 cuz it's pinned, and an easier way is simply Rh7

if you let the the rook stand on c1, then all black has to do Qe3+. and the bishop white queen can't do anything cuz it's pinned, and after the white king moves, the black queen is free to remove the white queen and checkmate is easily avoided, so it's better to use Rg2, since it's a forced move. 

making moves like  Rc1 is simply risking it 

aaamaximum wrote:

queen can't do g2 cuz it's pinned, and an easier way is simply Rh7

if you let the the rook stand on c1, then all black has to do Qe3+. and the bishop white queen can't do anything cuz it's pinned, and after the white king moves, the black queen is free to remove the white queen and checkmate is easily avoided, so it's better to use Rg2, since it's a forced move. 

making moves like  Rc1 is simply risking it 

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It's not risky, it's flat-out losing.  And please note the elipsis in my reccomendation for Qg2+.  An elipsis(three dots ...) denotes a move by Black.  As the Black queen is not pinned, this move is perfectly fine.  Also, when does the rook have an opportunity to move to g2?  I give your post a D+.

There is a forced checkmate after 1.Rh7+ Qxh7 2.Qxe1# The answer to the puzzle also does not work because Qg2+ and black wins.

1...Qd3+ also works for black

Not arguing with silentfilmstar, just what I saw 1st, before reading his input.  It is actually kinda interesting that Rh7 works as I tended to eliminate it as capturable, and only reconsidered it when I realized that white had to check black (as black has several available ways of checking white) and Rh7 is white's only way of doing so.