general topology – $S^{1}$ is locally euclidean

Prove that the subspace $S^{1}={{(x,y)in mathbb{R^{2}} : d((x, y),(0,0))=1}}$ with $d$ the euclidien metric on $mathbb{R^{2}}$ is locally euclidean..
Let $(x,y)in S^{1}$ such that $(x,y)not= (1,0)$.
Then $(x,y)in S^{1}setminus{{(1,0)}}=mathbb{R^{2}}setminus{(1,0)}bigcap S^{1}$ open in S^{1} and we now that $S^{1}setminus{{(1,0)}}$ is homeomorphic to $)0,2pi($.
Now for {(1,0)} I can’t seem to find an open subset of S^{1} that contains (1,0) and homeomorphic to some open subset of $mathbb{R}$..any help please.