B+K vs. R+K Endgame

I posted on this endgame a long time ago, but I feel as though my conclusion may have been incorrect. At first I thought that, in an endgame with king+rook vs. king+bishop, the rook and king would win. This worked when the king and bishop were on the edge of the board, but when I tried it where the king and the bishop were at a corner of the board, I couldn't figure out what to do while still avoiding stalemate.

[Fen]8/8/8/8/8/4K3/8/1R1bk3[/Fen]

With white to move:

1. Rc1 kf1
2. Rxd1
(the K+R vs. K endgame would follow)

But take the following position:

[Fen]8/8/8/8/8/6K1/8/3R2bk[/Fen]

If anyone can find moves (reasonable moves (especially for black), not blunders) for white that will mate, please post them.

Edit: For some reason, my fen examples are not appearing, even though they're posted correctly...I had to type them incorrectly to make anything appear at all.

Rook vs. Bishop
This endgame is generally drawn. The weak side's King heads for a good corner, where it cannot be dislodged by the strong side.

[Note: The terms strong side and weak side refer to the total relative value of the pieces on the board. In this example, the side with the Rook is the strong side.]

What is a good corner? This is one of the two corner squares opposite to the color on which the Bishop moves. Here are contrasting examples.

http://chess.about.com/library/weekly/aa02k30.htm

That's a great website; thanks for posting it.

Originally posted by wittywonka

[fen]8/8/8/8/8/6K1/8/3R2bk[/fen]

If anyone can find moves (reasonable moves (especially for black), not blunders) for white that will mate, please post them.

Edit: For some reason, my fen examples are not appearing, even though they're posted correctly...I had to type them incorrectly to make anything appear at all.

Originally posted by XanthosNZ
there is a limit of 1 fen diagram per post