Can a piece attack (capture) the piece holding the check?
Yes, if a piece gives a check you can capture the check giving piece if this is legally possible.
See the chess positions below:
In the left diagram above the white bishop gives a check. There is no piece around that could capture the check giving bishop, so the black king must move away from the check. Best move is to play Ke7. After this Black can develop his rook to f8 to start a counter attack along the f-file.
In the right diagram above the white bishop gives a check. Black can and should capture the check giving bishop with his knight playing 1…NxB.
This move would win a piece for Black. If White recaptures with his knight playing 2. NxN then the black king recaptures the knight.
Black would be a piece up after this and would have a big material advantage and a winning position. He just has to move his king to a safer place after this.
In the left diagram the white queen gives a check and attacks the black queen at the same time. Black should capture the queen playing 1…QxQ. If he would move the king away from the check then the white queen would capture the black queen and this means that Black would have lost his queen for nothing.
In the right diagram the knight gives a check. White can capture the check giving knight with his bishop playing 1.BxN Or he can move his king away from the check playing 1.Kg3. That is up to him. Both moves are good. The position would be even after this.
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