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What's 8 plus five (in digits only)?
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File: CircleTheorems It seems that there is a collection of "Circle Theorems" that get taught in schools maths. These are: * Know that the tangent at any point on a circle is perpendicular to the radius at that point; * Explain why the perpendicular from the centre to the chord bisects the chord (Year 10) * Prove and use the facts that: * The angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference, * The angle subtended at the circumference by a semicircle is a right angle, * Angles in the same segment are equal, * Opposite angles on a cyclic quadrilateral sum to 180° (Year 11) * Prove and use the alternate segment theorem (Year 11) That makes seven "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 "ThalesTheorem". I wrote a blog entry about that. * https://www.solipsys.co.uk/new/ColinsBlog2007.html#toc_name005 The remaining three I need to think some more about - I'm not even sure what 5 and 7 mean.