Filling region limited by circumferences using Tkz-Euclide

Question

I am trying to fill the region enclosed by three circumferences (the little one in the middle) using TikZ or Tkz-Euclide but I am unable to do so, even after looking at several examples.

Here's my MWE:

\documentclass[10pt]{scrartcl}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{calc,decorations.pathmorphings}

\begin{document}

\begin{tikzpicture}
\tkzDefPoints{0/0/A, 2/0/B, 1/1.73/C}
\tkzDrawCircle[R](A,1cm)
\tkzDrawCircle[R](B,1cm)
\tkzDrawCircle[R](C,1cm)
\tkzLabelPoints[below left](A)
\tkzLabelPoints[below right](B)
\tkzLabelPoints[above](C)
\tkzDrawPoints(A,B,C)
\end{tikzpicture}

\end{document}

For reference, I have consulted the following similar questions:

Filling a complex region with TikZ

Filling in an area enclosed by two arcs and a line

Filling region between two \draw Tikz

Filling a region in Tikz

How to color a region?

Answer 1

A solution using \filldraw:

\documentclass[10pt]{scrartcl}

\usepackage{tikz}
\usepackage{tkz-euclide}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}
\tkzDefPoints{0/0/A, 2/0/B, 1/1.732/C}
\tkzDrawCircle[R](A,1cm)
\tkzDrawCircle[R](B,1cm)
\tkzDrawCircle[R](C,1cm)
\tkzLabelPoints[below left](A)
\tkzLabelPoints[below right](B)
\tkzLabelPoints[above](C)
\tkzDrawPoints(A,B,C)
% This is my original answer:
\filldraw[fill=red]
  ($(A)!0.5!(C)$) arc (60:0:1cm) --
  ($(B)!0.5!(A)$) arc (180:120:1cm) --
  ($(C)!0.5!(B)$) arc (-60:-120:1cm) -- cycle;
% Or a much simpler version suggested by @marmot in the comments:
% \filldraw[fill=red] ($(A)!0.5!(B)$) arc(0:60:1) arc(-120:-60:1) arc(120:180:1);
\end{tikzpicture}

\end{document}