Black has no safe squares so he can't move his king, he cannot capture the rook so the only thing he can do is block the check.
I see 3 ways he can block, none of them are really appealing:
Bc5, Rxc5+ and check again
Qc3, Rxc3+ loses the queen and doesn't even blunt the attack.
Qc7 seems like the only move that doesn't lose outright. The next sequence would something like this: Qc7, Rxc7+, Kb8, Rd7+ threatening Rxd8#, Kc8, Rc1+ and the game is over at this point.
After ..., Nxc2, Rxc2+
Black has no safe squares so he can't move his king, he cannot capture the rook so the only thing he can do is block the check.
I see 3 ways he can block, none of them are really appealing:
Bc5, Rxc5+ and check again
Qc3, Rxc3+ loses the queen and doesn't even blunt the attack.
Qc7 seems like the only move that doesn't lose outright. The next sequence would something like this: Qc7, Rxc7+, Kb8, Rd7+ threatening Rxd8#, Kc8, Rc1+ and the game is over at this point.