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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 link

The Quintessential Proof live

Stage: 5 Challenge Level: Challenge Level:1

In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.

Quadrature of the Lunes link

Quadrature of the Lunes live

Stage: 5 Challenge Level: Challenge Level:1

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 link

Finding Circles live

Stage: 5 Challenge Level: Challenge Level:1

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 link

The Circle of Apollonius... Coordinate Edition live

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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