Circle Theorems 


The first and second follow from symmetry. The third is quite tricky to find a proof of, and could give a real "Aha!" moment. The fourth is a simple deduction from the third, and is known as "Thale sTheorem".
I wrote a blog entry about that.
The remaining three I need to think some more about  I'm not even sure what 5 and 7 mean.
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Quotation from Tim BernersLee 