What is the main idea in this winning endgame? I was playing an online game with the white pieces and won the exchange in the middlegame. So I exchanged some pieces and went for the &quot;winning endgame&quot;. I went ahead to draw the game. Afterwards, I analyzed the game and the Lichess analyzer showed that I had +1.8 advantage in this position.
[Title &quot;White to move&quot;]
[fen &quot;B7/3R2p1/4pk2/2p2p2/Pb3P1p/4P1P1/2b4P/6K1 w - - 0 41&quot;]

I want to know what is the best strategy here to take advantage of my rook over Black's bishop. I figure my bishop should by in the same diagonal my passed pawn, so 42.Bc6 seems like a good continuation, so black responded with 42. ...h3, now my king is somewhat trapped by Blacks bishops, and they are too active, I do not have enough time to make my rook guard the a5 square so that I can push my pawn. So what should I be rooting for in this position? How to activate my king?
Interesting position;
Activating your king I don't believe is the answer. I think your first goal is try and force the the c2 bishop off the board. corner the black king and create as many potential promotion threats (a , e and h files particularly)
I played the position out for a while on a few variations and will attach the cleanest variant;
I see the main objectives for white though is to try and lock blacks king on the right hand side and or rear of the board, try and remove potential promotion threats. Black black bishop is relatively harmless and is tied to the c5 pawn. Preventing the c5 pawn from promoting or moving will also keep the b4 bishop from being active in the game. Slowly whittle down the right side of the board which creates to many promotion opportunities that overwhelms blacks defenses.
[Title &quot;White to move&quot;]
[fen &quot;B7/3R2p1/4pk2/2p2p2/Pb3P1p/4P1P1/2b4P/6K1 w - - 0 42&quot;]

1. Bc6 h3 2. Kf2 g5 3. Rb7 gxf4 4. gxf4 Kg6 5. Be8+ Kh6 6.Rb6 Kg7 7. Rxe6 Kf8

Key Moves:
gxf4 by capturing towards the center, you keep the b4 bishop not being able to cause any impact to whites pawns on the E through H files. Any attempts will result in a loss of material. In addition to this the c2 bishop is quite an inactive piece in this position
[Title &quot;White to move&quot;]
[fen &quot;4Bk2/8/4R3/2p2p2/Pb3P2/4P2p/2b2K1P/8 w - - 0 8&quot;]

8. Bd7 Bb3 9. Ra6 Bd5 10. Be6 Be4 11. Ra7 Ke8 12. a5 Bd3 13. a6 Bxa6 14. Rxa6 Bc3 15. Rc6 Bb4 16. Bxf5 Kf8 17. Bxh3 Kg7

Key Moves
Be6 support by the rook on a6, white has no means of capturing the without trading out its only useful bishop. The bishop is also somewhat &quot;shepherding&quot; the king with the a6 rook. It is also positioned attacking the c8-e3 diagonal poised to take out blacks pawns and threaten promotion.
Ra7 Locks the king to the d8 , e8 , f8 squares.
a6 forces black to capture with the bishop otherwise white can easily promote to queen and then mate.
To summarize

Blacks b4 bishop is tied to the c5 pawn. Blacks only potential promotion threat can be largely ignored.
Keep up pressure. This is preventing Black from doing any meaningful development. Black is forced to move and lose pieces in this position.
Prevent Black from activating their king.