Since we want to have max. no of circles, we assume that no three points are co-linear. Having that said, Circles can be formed from any four points in 7C4 ways and now we have to subtract those circles which are made from 5 points & 6 points & all 7 points. (There will be over lapping cases in these too.)
We have not been taught sets, venn diagram. If someone has been taught that, give this method a try.