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### Advanced mathematics

# Circular Arguments

### The Quintessential Proof

### Quadrature of the Lunes

### Finding Circles

### The Circle of Apollonius... Coordinate Edition

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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!

Age 16 to 18

Challenge Level

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

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?

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?

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?