You may also like
Fixing It
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
OK! Now Prove It
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?
Summats Clear
Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
Age 16 to 18
Challenge Level
A triangle $ABC$ is inscribed in a circle with $AB$ as diameter. Find the maximum value of $AC + CB$.
Now generalise your result to the case where $AB$ is fixed but not a diameter of the circle.
Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius $r$ that has the maximum perimeter and the maximum area.
Copyright © 1997 - 2022. 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.