user8208: 
Why can the white king not take the queen here?

user7726: Because that would move the king into check - the queen is defended by the bishop on c5.
More generally there is no problem with a king taking a piece that is checking it, provided the capture does not move the king into check or break any of the other laws of chess.

8208: <p><a href="https://i.stack.imgur.com/uF1lD.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/uF1lD.jpg" alt="enter image description here"></a></p>

<p>Why can the white king not take the queen here?</p>
 7726: <p>Because that would move the king into check - the queen is defended by the bishop on c5.</p>

<p>More generally there is <strong>no</strong> problem with a king taking a piece that is checking it, <strong>provided</strong> the capture does not move the king into check or break any of the other laws of chess.</p>
