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If a king is in check, can the opponent's king take said king if it puts them in check? Someone may think they win, but surely you can’t put yourself in check even if the opponent's king has been taken.

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It's not possible to get into a position where you can take his king. He must have made a move that left him in check, and that's illegal.

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I assume you mean something like the following: white king is on h1, white bishop is on g1, black rook is on a1, and black king is on a7, and it's black's turn to move. If black doesn't move the king, then the bishop can capture him ... but that would expose the white king to check. In this case, the black king still has to move, even though white can't capture him without putting the white king in check. White wouldn't ever get a chance to capture the king, because not moving the king would be an illegal move.

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Even if it were legal you would no longer be able win because without an opposing king you would have no possible checkmate.

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You cannot capture king in chess. Check mate is not capturing the king. The game ends when king is under attack, and cannot escape. Any move that leads king to be captured is illegal.

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