Circle Theorems

Reasons carry the marks

• Many circle questions ask for an angle and the theorem that justifies it, with a mark for each
• On some questions the reason is a whole part on its own, so the wording has to be right
• Where the answer takes two steps, two reasons are expected: give one for each step, not just the last one
• The ordinary angle facts stay available throughout: angles in a triangle, angles on a line, angles at a point, isosceles triangles and angles in a quadrilateral
• Mark the radii on a diagram first, since any two of them make an isosceles triangle and that is often the missing step
• Diagrams are not to scale, so never measure

The theorems you need

• Two angle theorems are examined: the angle in a semicircle is 90°, and the angle between a tangent and a radius is 90°
• The ordinary angle facts above do the rest of the work, so a question is usually a short chain of those with one circle theorem in the middle