After execute the snap settings toggle to the needed durable preferences. Grid > snap pivot with absolute grid alignment Place > objectmode: snap object to surface of other objects Retopo > editmode: snap selected onto target surface Cursor > set 3d cursor to active or selected Closest > snap...
or three vertices (not required to be adjacent) this operator will places the 3d cursor at original center of that circle. updated version may become a modal operator to generate a full set of circle vertices, with variable vertex count. ...