You may also like
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.
Simultaneous equations. Sine rule & cosine rule. Inequalities. Creating and manipulating expressions and formulae. Pythagoras' theorem. Similarity and congruence. Regular polygons and circles. Circle properties and circle theorems. Mathematical reasoning & proof. Polynomial functions and their roots.
Copyright © 1997 - 2019. University of Cambridge. All rights reserved.
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.