Place a Rook

In the following diagram, where can White place a rook in order to have a drawn position with Black to move?

I found a game with this position and a White rook on h8 using the report feature of ChessBase 17. I had been playing with a position derived from Ending 57 in 100 Endgames You Must Know by Jesus de la Villa. Aside from the position that he presents, I wanted to understand where else the rook might be placed and still draw.

De la Villa's Ending 57 has this position with White to move.

After 1.Rd8, Black has two moves that hold a draw.

Before looking at de la Villa's solution, I placed Black's rook on a1 and made White's move Rd8. Then, I played Black against Stockfish on my iPad, trying a couple of variations. Then, I checked my ideas with ChessBase.

This was one of the resulting positions.

Black to move

4...Ke6 is the only drawing move.

This was another position in my play against the engine.

Black to move

Here, the side check is Black's only chance. 2...Ra7+

Using the report > similar endgames feature of ChessBase turned up far more games than I have time to look through. I favored those that were decisive, certain that I could find examples of games where a player who could have drawn instead lost.

No doubt both players were in considerable time pressure when Black erred from this winning position.

Black to move

Black played 110...Rf1?? 

110...d2 wins. To wit, 111.Re8+ Kf4 and White soon runs out of checks.

Nonetheless, Black won the game because his young opponent missed the drawing idea.

In the diagram at the top of this post, where must White place the rook?