I want to draw something like this : an eye with an arc.
I started like this but I don't know how to continue
\documentclass[reqno]{amsart}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (0,0) arc(0:-180:3);
\draw[very thick,yshift=6cm](-3,0) .. controls (-2,2) and (2,2) .. (3,0) .. controls (2,-2) and (-2,-2) .. (-3,0)--cycle;
\end{tikzpicture}
\end{document}
