Tex + Tikz, 232 bytes

43 bytes saved by switching to tex. Thanks to Phelype Oleinik

A byte saved thanks to Skillmon

\input tikz \tikz[x=1,y=1,white]{\def\f{\foreach\1in{90:,210:,330:}}\def\u{\draw[line width=}\def~{circle(}\f\fill[red](\122)~30);\f{\u2](0,)--(\111);\u8](\130)--(\160);\fill(\130)~21);}\fill~6);\u7,red]~23.5);\f\u2](\130)~20);}\bye

With line breaks and without \def:

\input tikz
\tikz[x=1,y=1,white]{
\foreach\1in{90,210,330}\fill[red](\1:22)circle(30);
\foreach\1in{90,210,330}{
\draw[line width=2](0,0)--(\1:11);
\fill(\1:30)circle(21);
\draw[line width=8](\1:30)--(\1:60);
}
\fill(0,0)circle(6);
\draw[line width=7,red](0,0)circle(23.5);
\foreach\1in{90,210,330}\draw[line width=2](\1:30)circle(20);
}
\bye

Explanation

This is a little outdated I will fix it when I can figure out how to make the images not enourmous

Here I am going to explain how the uncompressed answer solves the problem. I may at some point explain how the compression works. First we draw the big black circles:

\foreach\x in{90,210,330}\fill(\x:21)circle(30);

Then we draw some white lines:

\foreach\x in{90,210,330}\draw[white,line width=2cm](0,0)--(\x:11);

Then we draw white circles:

\foreach\x in{90,210,330}\fill[white](\x:30)circle(21);

Then we add a central white circle:

\fill[white](0,0)circle(6);

Then we add a black annulus:

\draw[line width=7cm](0,0)circle(25.5);

Then we remove parts of the black annulus

\foreach\x in{90,210,330}\draw[white,line width=2cm](\x:30)circle(20);