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In other words, after white's move, black king is not in check. It is now black's move, but any move that black could make results in check. Is this a checkmate? Is there a chess term for this situation?

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up vote 14 down vote accepted
  • Putting your king in check is not a legal move as you've realized.
  • Of course, if Black has any OTHER legal moves he can and should play one of them!
  • If a side TO MOVE does not have ANY legal moves, that would be a stalemate, not a checkmate (which is delivered only by the side making the check)
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...and stalemate means the game ends as a draw. – RemcoGerlich Mar 9 '14 at 9:00
Which means that white just screwed him/herself out of a victory. Oops. :) – Shadur Mar 9 '14 at 12:45
There are some endgame positions where stalemating the opponent prevents you from losing, so stalemate can be something worthy to achieve for the one who does. – chaosflaws Mar 18 '14 at 13:31

It's called a stalemate, which is a draw.

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No, if there are no more moves available to black then it is a stalemate.

If black has other pieces which have moves available to them they must move those pieces.

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