0580

Circle Theorems

Geometry

Flashcards

Reasons carry the marks

  • Circle questions ask for an angle and the theorem that justifies it, with a mark for each
  • On many 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: mark schemes ask for one for every angle found, 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
A circle with centre O and points A, B and C on it, all joined to O and to each other: the angle BOC at the centre is 150 degrees and the angle at B is 60, and because OA, OB and OC are all radii the triangles inside are isosceles, which is what unlocks the angle x at A
Source: Angles at centre & circumference by Save My Exams
  • Diagrams are not to scale, so never measure
Exam tip

Give a reason for every angle you find, not just the last one. Where the chain takes two steps the scheme expects two reasons, and "give a reason for your answer" is printed in 11 of the 43 papers. Name the theorem in full: an abbreviation on its own is not accepted.

The theorems you need

  • Six angle theorems are examined: the angle in a semicircle, the angle between a tangent and a radius, the angle at the centre, angles in the same segment, opposite angles of a cyclic quadrilateral, and the alternate segment theorem
  • Three further symmetry properties finish the list, and they are gathered in the last section of this note