allowable king moves

Can a king ever move into a place where he can be taken

no

If an enemy piece (a Bishop) is pinned on its own King, can my King move into the Bishop's path of attack?

I think my King can move into the Bishop's path of attack because the Bishop, in order to capture my King, would involve my opponent "moving into check," which is illegal.  To imagine the logic, it is:  As soon as the Bishop would infinitesimally expose its King to check as the Bishop would begin to travel off its square, the illegality of the Bishop move occurs.

What say you?

Solved my question, with a little bit of ingenuity, for myself.

I cleaned up my relic Fidelity Elite Avant Garde 2265 wooden auto-sensory chessboard, put it into PB (Problem Mode) and set up the pieces to replicate my above-post hypothetical position.  Then I tried moving my King into the path of the Bishop that was pinned on its King.  The Elite Avant Garde double-beeped an "illegal move" sound.

So, now I know, positively.

An attacked square, even if the attacking-square-piece is pinned-absolutely on its King, cannot be moved onto by your King.  You would be moving into check:  illegal move by you.

That's right. As in the example below, the white king is in check but cannot move to f1 or f2 because of the rook on f7. It doesn't matter that the rook on f7 is itself pinned. One way to think of it is that of the king went to f1 and the black rook captures, the rook would capture the king before the white bishop would capture the white king.

corum, good example.

But edit your post toward the end, where you're talking about Queens that are really Bishops.

Doh!! Thanks

corum, you're not out of the woods, yet.

is that of the King… change to… is that if the King.

white bishop would capture the white king… change to… white bishop would capture the black king

Being a little picayune here, but I want this thread to endure.

Asked and answered. Corum's #5 example shows why.