Castlerigg stone circle, located near Keswick in Cumbria, England, is one of the most important prehistoric monuments in Britain. To determine the approximate date of its construction, we can look at archaeological studies and historical context.

Based on current archaeological evidence, Castlerigg stone circle is believed to have been constructed around 3000 BC. This places it in the Neolithic period, a time when humans were transitioning from a nomadic lifestyle to more settled agricultural communities.

To summarize:

• 3000 BC: This is the widely accepted date for the construction of Castlerigg stone circle.
• 2000 BC: This date is too late for the construction of the circle, as it is generally associated with later Bronze Age structures.
• 1000 BC: This date is also too late and does not align with the Neolithic period when the circle was built.

Thus, the correct answer is 3000 BC.