\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[help lines] (0,0) grid (4,3);
\draw [blue]([shift=(60:5pt)]0,0){}--+(30:1cm) arc(30:90:1cm)--cycle;
\draw [red](0,0)--(90:1cm) arc(90:390:1cm)--cycle;
\end{tikzpicture}
\begin{tikzpicture}
\draw[help lines] (0,0) grid (4,3);
\draw [blue]([shift=(30:5pt)]0,0){}--+(30:1cm) arc(30:90:1cm)--cycle;
\draw [red](0,0)--(90:1cm) arc(90:390:1cm)--cycle;
\end{tikzpicture}
\begin{tikzpicture}
\draw[help lines] (0,0) grid (4,3);
\draw [blue]([shift=(90:5pt)]0,0){}--+(30:1cm) arc(30:90:1cm)--cycle;
\draw [red](0,0)--(90:1cm) arc(90:390:1cm)--cycle;
\end{tikzpicture}
\end{document}