# Circle Theorems

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 "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.