• 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)

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.

• https://www.solipsys.co.uk/new/ColinsBlog2007.html#toc_name005

Quotation from Tim Berners-Lee