The Secret Word - Puzzle

A teacher writes six words on a board: “cat dog has max dim tag.” She gives three students, Albert, Bernard and Cheryl each a piece of paper with one letter from one of the words.

Then she asks, “Albert, do you know the word?” Albert immediately replies yes.

She asks, “Bernard, do you know the word?” He thinks for a moment and replies yes. 

Then she asks Cheryl the same question. She thinks and then replies yes. 

What is the word?

THIS must be the given word!