Fitting in

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F 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
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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 $AB = 5EF$.

Image
Fitting In

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 $LM = 3PQ$.

Image
Fitting In