Is word ‘imaginary’ used much in English in specific situations? For example, I run in a circle on the playground, but actually there are no real circles. In this case, is ‘imaginary’ used such as in ‘I run in an imaginary circle on the playground’?
The word "imaginary" is used all the time in English, depending on context, as Kman commented. In some disciplines of math, for example, the concept of "imaginary numbers" is very important and is very heavily discussed. But in other disciplines the concept does not come up. People talk about having "imaginary friends." Someone describing a radio signal might compare it to an "imaginary line" coming off the antenna.
In your context, running around in circles where there is no circle marked, "imaginary circle" could be used and would sound perfectly fine. Another option might be "invisible circle" or "unmarked circle."