The names

  • A radius is a straight line from the centre to the circle. A diameter is a chord that passes through the centre, so it is two radii long.
  • A chord is a straight line joining two points on the circle. A tangent is a straight line that touches the circle at exactly one point.
  • An arc is part of the circumference. A sector is a region bounded by two radii and an arc (a slice of pizza). A segment is a region bounded by a chord and an arc.
Osectorradiuschordtangent

Two radii make an isosceles triangle

Every radius of a circle is the same length. So if A and B are on a circle with centre O, OA = OB and triangle OAB is isosceles: angle OAB = angle OBA. This one fact is behind every circle theorem in the next lesson, because base angles of an isosceles triangle are equal.

  1. angle AOB = 110°
  2. angle OAB = angle OBA = (180 − 110) ÷ 2 = 35°

The same idea gives equations: if OA = (2x + 5) cm and OB = (4x − 3) cm, they are both radii, so 2x + 5 = 4x − 3.

First question