Queen vs. rook...checkmate?!

Queen vs. rook...checkmate?!

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Is it possible to win in an endgame where you have a queen and your opponent has a rook? I think I once got into this kind of situation, and got a draw.

Seems to me it should be a draw:

Unless I made bad moves in the diagram above, it should be a draw, at least from the starting position above. What do you think?

--GSHAPIROY

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