White is considering Ne5. A good idea? No; for it is important to notice any discovery kernels your opponent has, not just your own. Here Black’s bishop on b7 is masked by his pawn on c6, and this represents a major threat to White on the long diagonal. While White’s king isn't on that diagonal at the moment, he has to be wary of any moves that would expose him to sequences following the general pattern seen several times above. If White's knight moves, it clears a piece from that diagonal and the only thing then standing between Black and a discovered check is the need to draw the king onto g2—accomplished easily enough by capturing the pawn on that square and forcing a recapture with Qxg2+. After KxQ, Black plays c6-c5, winning back the queen and netting a pawn.
It might have occurred to you to worry as well that after White’s Ne5, Black would play the discovered mate threat c6-c5—threatening Qxg2# without needing to move White’s king into position. But this is another of those cases where a mate threat is not as effective as a check because it leaves White time to take the initiative with a check of his own: Qxd7+, with protection from the knight (which by then is on e5). After Black’s king moves, White has NxQ. So Black is better off replying with 1. ...Qxg2 as described above—and you are better off assuming your opponent will play the smart response to whatever you do.
This batch of studies nicely illustrates the power of a fianchettoed bishop—in other words, a bishop moved from its original square to b2 or g2 (for White) or b7 or g7 (for Black).