It's a real art to make logo of just arcs of minumum number of circles, here is one great example from my colleague

out of 36,000 logos sent to the team of LogoLounge, LogoLounge – a collection of the world’s best logotypes – the panel of judges selected top 20. Among the highest ranked 20 logos, there it was: this work done for FishMarket– a red crab entirely constructed from various circular arcs.