Here is an additional trick once you have learned to circular breath. Many times we have to play repeated articulated notes without a break to breath. I can think of a few solo works, George Perle's 3 Invertions, the third movement. There are some breaks, but longer stretches sound better, ( the first and second movements have 3 high G's). Shulhoff, the Bass Nightingale ( for contra) also has a movement that would be easier with the technique. In the beginning upward melodies above the staff are easier places, (more resistance). I have used it in the orchestra a few times, we had a modern work that had a repeated note section without anywhere to breath and it helped keep the line going, ( I think I used it in a Mahler symphony too, it was loud enough that breathing would not have hurt anything, but it is good to practice not getting noticed when you do it). I used to think it was impossible, but our principal oboe said he could and he inspired me to learn it. I doubt it can be done while double tonguing, but I bet someone might be able to. The only fast articulation I can think of while doing it is the jazz technique of flubble tongue, that technique doesn't use the back of the tongue like double tongue and circular breathing do, just the tip.
Principal bassoonist, Orquesta Sinfonica de Galicia, A Coruña, Spain. Bassoonist, bassoon dad, bassoon husband, bassoon uncle, bassoon brother and bassoon son.