They both contain "used to" but they are not both just "used to".
"used to" = did (something) in the past.
"be used to" = to be accustomed to (something)
The first is followed by the bare infinitive. (I used to live alone.)
The second is followed by a noun phrase or gerund. (I am used to the solitude/I am used to living alone.)
To expand on what other people have said, B is wrong because the structure is "is used to living". C is wrong because it lacks "is." When "to be" is missing, we use an infinitive. If C became "used to live," then that would be correct.