This year the tenth of Teves falls on a Sunday, which happens to also be an NFL game day. Is it permissible or discouraged to attend such a sporting event during the fast?
The Mishnah Brurah (549:1) explains that the main point of a fast is to do teshuvah, and not the fast itself: By Ninveh, concerning G-d undoing the decree to destroy them, it says "And G-d saw their actions," not "And G-d saw their fast." The fast is merely a preparation for the teshuvah. He continues, quoting the Chayei Adam, that those people who spend the whole fast on a trip or in idle speech while still fasting are fulfilling the secondary purpose (fasting) but not the primary one (theshuvah)!
So although it's technically permitted, the Mishnah Brurah discourages it. (NFL games can always be recorded :).)