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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
Triangle Midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Age 14 to 16 Challenge Level:
This printable worksheet may be useful: Nicely Similar.
This is an important construction on a right-angled triangle. The hope is that cast in the form of a problem this structural relationship will emerge to surprise those who haven't seen it before, and provide some challenge for those who have.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.