\documentclass[border=0]{standalone}
%\documentclass[12pt]{article}
\usepackage{tikz,tkz-euclide}

\definecolor{sauron}{rgb}{1, 0.4980, 0.0980}
\definecolor{uef-turquoise}{rgb}{0, 0.654902, 0.709804}
\definecolor{uef-gray}{rgb}{0.254902, 0.294118, 0.345098}

\begin{document}

\def\sqrttwo{1.4142135}
\begin{tikzpicture}
\path [clip] (0,0) circle (1.1cm);
\filldraw[uef-turquoise] (0,0) circle (1cm);
\begin{scope}
\path [clip] (0,1) circle (\sqrttwo cm);
\filldraw[black] (0,-1) circle (\sqrttwo cm);
\end{scope}
\end{tikzpicture}

\end{document}