ところtokoroga
1.

A conjunction used to introduce a statement that contrasts with or qualifies a previous one, indicating a surprising or unexpected outcome.

2.

A phrase that emphasizes a turn in conversation, often suggesting that the subsequent information may oppose or provide an alternative perspective to what has been stated earlier.

3.

A connector that indicates an acknowledgment of a previous situation but introduces an assertion that changes the context or expectation of the discussion.

4.

A term used to denote a sense of continuation or persistence in a situation, implying that despite preceding circumstances, another facet or outcome is presented.

Example:

ところが実はどうすることもできないのです。