It seems that there is a collection of "Circle Theorems" that
get taught in schools maths. These are:
That makes seven "Theorems".
- 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
- 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)
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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