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?

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?