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Theorem 1

Theorem 2

Theorem 3

Theorem 4

Theorem 5

Theorem 6

Theorem 7

The Seven Theorems

## Dynamic Geometry & Circle TheoremsI've set out these pages so that either you can use them to work out what the theorems are, or you can just go to 'The Seven Theorems' page where they're lurking with suitable diagrams. Or here where you can download a .pdf file which summarises the theorems - a hard-copy version of 'The Seven Theorems' page. But try out the dynamic geometry pages first!!! Geogebra is a free dynamic geometry package, very suitable for illustrating the circle theorems. As it is dynamic geometry, you can move points around and see what happens! Here are GeoGebra Dynamic Worksheet pages with the seven circle theorems (as used in the UK's GCSE Maths exams!!) - First circle theorem - angles at the centre and at the circumference.
- Second circle theorem - angle in a semicircle.
- Third circle theorem - angles in the same segment.
- Fourth circle theorem - angles in a cyclic quadlateral.
- Fifth circle theorem - length of tangents.
- Sixth circle theorem - angle between circle tangent and radius.
- Seventh circle theorem - alternate segment theorem.
Tim Devereux [Page updated 25/01/13] |