What are some words that have the word tact in it?

You're right, "tact" isn't a very common word root. Here are some words with the root "tact" that you may come across:

* Tactile: Relating to the sense of touch.

* Tactual: Same as tactile.

* Tactilian: Relating to the sense of touch.

While "tact" isn't as common a root as, say, "bio" or "geo", it does appear in some specialized vocabulary, particularly in the fields of biology and psychology.