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Part of 1990 Flanders Math Olympiad

Problems(1)

bourgondian cross (I think)

Source: flanders '90

On the standard unit circle, draw 4 unit circles with centers [0,1],[1,0],[0,-1],[-1,0]. You get a figure as below, find the area of the colored part. http://www.mathlinks.ro/Forum/album_pic.php?pic_id=277