Circular Arguments

Circular arguments

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!


The Quintessential Proof 

Age 16 to 18
Challenge Level
In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.

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?

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?
Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?