quick question making circle coincident with corner

Hi All,

Quick sketching question.  I need to get the circle on attached sketch coincident with the corners of the rectangular tube while still maintaining the center / midpoint relationship between the two.  I can trig it out to get close but then when I go to cut extrude, I get some weird pieces still there.  Not sure what relationship to add at this location.  Thanks!

SolidworksSketching