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## 'Fitting In' printed from http://nrich.maths.org/

The largest square which fits into a circle is $ABCD$ and $EFGH$
is a square with $E$ and $F$ on the line $AB$ and $G$ and $H$ on
the circumference of the circle. Show that $AB = 5EF$.

Similarly the largest equilateral triangle which fits into a
circle is $LMN$ and $PQR$ is an equilateral triangle with $P$ and
$Q$ on the line $LM$ and $R$ on the circumference of the circle.
Show that $LM = 3PQ$.