From The Book of Our Heritage by Rabbi Eliyahu Kitov...
Three fast days are observed during the month of Tevet, commemorating three calamities which befell Israel - on the eighth, ninth, and tenth days of the month. The fast days of the eighth and ninth are referred to as "fast days for the righteous." On these days, only individuals fast, whereas the fast on the tenth of Tevet is a public fast day for the entire community.
The fast of the eighth of Tevet commemorates the day when the Torah was translated into Greek at the order of King Talmai (Ptolemy). The Sages note that the day on which the Torah was translated into Greek was as calamitous for Israel as the day on which they made the golden calf, for it is impossible to translate the Torah adequately.To be continued...