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Moybologue Church is a very interesting medieval ruin located near Bailieborough, in County Cavan. The church is dedicated to St. Patrick, who is believed to be a founder of an early Christian temple here, in the 5th century. The graveyard has many noteworthy headstones and grave markers, as well as early medieval cross slabs and grave slabs.
http://directionireland.com/index.php?obj=Moybologue%20Church&id=297

The 12th-century Kilcooly is one of the finest Cistercian Abbeys in Ireland and a great example of Gothic architecture. It is located in the village of Gortnahoe, in County Tipperary
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Shronebirrane Stone Circle, Co.Kerry
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County Cavan Museum features a wide range of artefacts dating from the Stone Age up until the 20th century. Among the most interesting exhibits are pre-Christian three-faced Corleck Head, a 1000-year-old dugout boat, or a collection of medieval Sheela-na-Gigs. A very important feature of the museum, attracting many visitors, is the outdoor replica of World War I trenches.
http://directionireland.com/index.php?obj=County%20Cavan%20Museum&id=287