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can a piece that can't be moved protect another piece

Can a piece that can't be moved protect another piece? An example: Does the black rook protect the black queen from the white king?
www.imgpaste.net/image/jSGBP

On the one hand I'd say "no" because of the black rook on g7. On the other hand I'd say "yes" because the black rook can't move. The solution of the puzzle (tz87r) gives the impression that the rook does protect the queen.
Good question! I'd like to know why that's how it works!
(The second paragraph is about "can the king take the queen".)
A pinned piece CAN check a king, the mentality being that if white takes it, then black could take the king before white would, and as putting your king in check isn't allowed, you would have to move your king out. It used to be considered the other way by some before the rules of chess were codified, but now, with FIDE's rules, capturing a protected piece is not allowed, even if that piece is pinned to the king.
You're right that black can't move the rook without putting himself in check.
But if white tried to capture the queen, white would be in check first. The rook does still cover that square. And since you're never allowed to put yourself in check, the black queen is safe from the king. Any other piece could capture the queen and laugh at the rook, just not the king.
In general the King loses it power versus other pieces since the opponents pinned piece still prevents the kings movement to the protected square(s). Is this fair? I assume the logic has been determined by Fide. Are there any documents/papers regarding this matter? It would be an interesting read.
White king can't capture the black queen so there is a protection in this special case.

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