These resources from the CMEP web site explore the properties of triangles and circles using coordinate geometry. Have a go at proving some geometrical connections, and prove Pythagoras's theorem in an intriguing way you may not have seen before!
problem
The quintessential proof
Age
16 to 18
Challenge level
In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.
problem
Quadrature of the lunes
Age
16 to 18
Challenge level
A lune is the area left when part of a circle is cut off by another circle. Can you work out the area?
problem
Finding circles
Age
16 to 18
Challenge level
Can you find the centre and equation of a circle given a number of points on the circle? When is it possible and when is it not?
problem
The circle of Apollonius... coordinate edition
Age
16 to 18
Challenge level
Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?
