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\begin{document}

%-------------------------------------------------------------------

\section*{six semi-circles in a circle solution}

\hypertarget{solution_to_the_six_semicircles_in_a_circle_puzzle}{}\section*{{Solution to the Six Semi-Circles in a Circle Puzzle}}\label{solution_to_the_six_semicircles_in_a_circle_puzzle}

[[SixSemiCirclesinaCircle.png:pic]]

\begin{quote}%
A semicircle drawn on each side of a regular hexagon. What fraction of the outer circle is shaded?


\end{quote}
\hypertarget{solution_by_lengths_in_a_regular_hexagon}{}\subsection*{{Solution by [[Lengths in a Regular Hexagon]]}}\label{solution_by_lengths_in_a_regular_hexagon}

[[SixSemiCirclesinaCircleLabelled.png:pic]]

The above diagram shows that each ``leaf'' can be folded to fit into a side of the central curved hexagon to exactly fill out the dark green circle. The radius of this circle is half that of the outer circle, so its area is one quarter of that of the outer circle.



\end{document}