I have very limited LaTeX knowledge. I am trying to plot the following figure using "tikz" and I appreciate if anyone can help me to finish plotting my figure. I did the following so far:

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}

\draw (0,0) arc (0:180:6);
\draw   (-12,0)  - -(0,0);
\draw (-8,0) arc (0:180:2);
\draw (0,0) arc (0:180:4);
\draw (-6,-0.1) - - (-6,0.1);

\end{tikzpicture}

\end{document}


There is a BIG semi-circle and two inner SMALL semi-circles. I want to label the right endpoint of the BIG semi-circle by "A" and  the left endpoint of the BIG semi-circle by "B". I want to label the center of the BIG semi-circle by "O", and I want to label the point where the two SMALL semicircles meet by "P". I also want to shade the area inside the BIG semi-circle and outside the two SMALL semi-circles. I also want to mention on the figure that the radius of the big circle is: 6. and the distance between the point "O" and the point "P" is "x"

Any help is much appreciated


Question: Past perfect sentence in "I would have killed the snake if I had hit him..."
Answer: It is a perfectly normal English construction and is an example of what foreign learners are sometimes taught as the Third Conditional. The speaker imagines something that didn't actually happen (in this case, he didn't hit the snake) and speculates what the consequence would have been if it had happened (he would have killed the snake).