# Specifying an arc without declaring a radius

I am trying to make are crescent shape like that shown below using two arcs. The code that I am using is:

\draw (0,0) arc [radius=5cm, start angle=270, end angle=450] node[pos=0](A){A} node[pos=1](B){B};
\draw (0,0) arc [radius=5.7735cm, start angle=300, end angle=420];

The downside of this is that I have to calculate the radius. Is there a way that an arc can be drawn by defining only (1) the terminal point coordinates and (2) the start and end angles?

An alternative is to use the in=<angle>, out=<angle> options:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\draw
(0,0) node (B) {B} to[out=-30,in=30]
(0,-8) node (A) {A} to[out=0,in=0,looseness=1.7]
(0,0);
\end{tikzpicture}

\end{document}