List

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
problem

The quintessential proof

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

Quadrature of the lunes

Age
16 to 18
Challenge level
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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
problem

Finding circles

Age
16 to 18
Challenge level
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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?