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Tenth of Tevet (Hebrew: עשרה בטבת, Asarah BeTevet), the tenth day of the Hebrew month of Tevet, is a minor fast day in Judaism. It is a "low fast" observed from sunrise to sunset. The day has no relationship to Hanukkah, but it happens to follow that festival by a week. Whether the 10th of Tevet falls 7 or 8 days after Hanukkah depends on whether the preceding month of Kislev has 29 or 30 days in the relevant year.
Historically, the fast commemorates the siege of Jerusalem by Nebuchadnezzar II of Babylonia—an event that began on that date and ultimately culminated in the destruction of Solomon's Temple (the First Temple) and the conquest of the Kingdom of Judah (nowadays: southern Israel).
(... from Wikipedia on 2012-04-17 06:31:10)