A black circle is a term used by members of the Lucian branch of the Cahill family. When an area is designated as a black circle, no Lucians are permitted to enter the area except those granted permission by the Lucian branch leader.
Only one black circle appears in The 39 Clues, in the book of the same name. Lucian agent Irina Spasky sets a black circle around the Church on the Blood during the Clue Hunt in order to enter the Amber Room and retrieve the Clue, Amber, hidden in the room. However, two members of Team Seven, Madrigals Amy and Dan Cahill, infiltrate the black circle and take the Clue before Irina is able to collect it.