Of course rules and 'minimums' are guidelines. There are ways get perfectly usable photos out of less than ideal conditions. However they can become constrained based on situation, be far less reliable, and demand both an eye for the motion and exceptionally steady hands with a disciplined control.
Not every photo needs perfectly static sharp perfection. Study other photos and look how they use they use the physical mechanics of photography. I don't have any circus photos, but elements of a derby photo I took at practice Thursday night can be used.
This photo is taken at 1/25th of a second, f/6.3, and ISO 3200. Lighting in that arena is very ugly and hard to work with, and this image has minimal editing (It was a test shot with a brand new lens). You've probably seen panning shots before, but the core concept of how they work can be applied in other ways. (Panning is just by far the easiest method of this.)
So while her face and shoulders aren't perfectly sharp, and I would love to be able to get them sharper, they are arguably acceptable sharp. This is in part due to just how blurry the rest of the image is, and I think that if the rest of the image was only as sharp as her face then it would not be acceptable to my standards now.
But what is actually going on here? Photography is collecting light information over relative space and time. I can avoid everything being affected by motion blur by keeping part of the main subject nearly stationary relative to my camera lens. This is done by panning with them, following their motion (And in this case taking photos as I go. This is the 4th of 6 photos I think. The others were unusable as she was shifting too much during the turn.)
And remember that it is time and space we're recording. If you look in the background you can see that there are three groups of five vertical bars behind her. Well, apparently there are five in each group, but light changes over time and in this case rather drastically. The lighting in this arena pulses up and down by over a stop, and those 'five' bars are each merely the same bar at five different points in time where the light was at its peak as the bar moved through the space relative to the camera lens.
You can play with this concept, learn to use it, and to judge relative motion. Once you better understand what is going on with it then you have a new tool you can use to create interesting photos by deliberately abusing this property of light and time.