drawing "trifecta" color mixing set

Question

I want to illustrate overlaps in three sets, similar to how one of these standard color plots [do they have a name?] look like

except that I want to choose my own colors and different text [not C, M, and Y]. (I want the inside most quasi-triangle to be a red, the area outside of the plot to be a green, and the partials [both three inner and three outers, though different] have some sort of mix colors. presumably a little bit lighter, because I need text in each intersection, too, that needs to be readable.). the idea is to show that when all three things come together, it's bad. a trifecta.

maybe I need a graphical artist rather than latex...or is this somehow built in?

Answer 1

It is actually quite easy to draw the single segments directly using polar coordinates and some arcs. There is no need to calculate intersections in a complicated manner. This way, you can style each segment as you wish. I leave it to you to place the nodes for the labels:

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
% upper circle segment
\path[fill=red!50] (180:1) 
    arc[start angle=180, end angle=0, radius=1]
    arc[start angle=60, end angle=120, radius=1]
    arc[start angle=60, end angle=120, radius=1]
    -- cycle;

% lower left circle segment
\path[fill=blue!50] (180:1) 
    arc[start angle=120, end angle=300, radius=1]
    arc[start angle=240, end angle=180, radius=1]
    arc[start angle=240, end angle=180, radius=1]
    -- cycle;

% lower right circle
\path[fill=green!50] (0:1) 
    arc[start angle=420, end angle=240, radius=1]
    arc[start angle=300, end angle=360, radius=1]
    arc[start angle=300, end angle=360, radius=1]
    -- cycle;

% inner pseudo triangle
\path[fill=gray!10] (0:0) 
    arc[start angle=60, end angle=0, radius=1]
    arc[start angle=300, end angle=240, radius=1]
    arc[start angle=180, end angle=120, radius=1]
    -- cycle;

% upper left pseudo triangle
\path[fill=magenta!50] (0:0) 
    arc[start angle=60, end angle=120, radius=1]
    arc[start angle=180, end angle=240, radius=1]
    arc[start angle=180, end angle=120, radius=1]
    -- cycle;

% upper right pseudo triangle
\path[fill=yellow!50] (0:0) 
    arc[start angle=120, end angle=60, radius=1]
    arc[start angle=360, end angle=300, radius=1]
    arc[start angle=0, end angle=60, radius=1]
    -- cycle;

% lower pseudo triangle
\path[fill=cyan!50, draw, thick] (240:1) 
    arc[start angle=240, end angle=300, radius=1]
    arc[start angle=360, end angle=300, radius=1]
    arc[start angle=240, end angle=180, radius=1]
    -- cycle;


\end{tikzpicture}
\end{document}