a number of paintings in the castle are believed___in a fire（动词不定式）

B.to have been destroyed
句型：
Sb/ Sth is believed/ thought/ considered/ reported/ said...+ 不定式（一般式, 进行式, 完成式）

说明： 此句型后面只能是不定式, 不可以是动词的ing 形式
再如：
He is said to be a student.
=It is said that he is a student.

The ship is reported to have sunk.
= It is reported that the ship has sunk.

She is believed to do doing her homework.
=It is believed that she is doing her homework.