Circles (SQA National 5 Maths): Revision Note

Relationship between the centre, chord and perpendicular bisector

What terms related to circles do I need to know?

• Circles have several specific terms that you need to be familiar with:

  • A circle's perimeter is called a circumference

  • Its line of symmetry is called a diameter

  • The line from the centre of the circle to its circumference is called a radius

    • The diameter is equal to 2 × the radius

  • A portion of the circumference is called an arc

  • A portion of the area, contained between two radii and an arc, is called a sector

  • A line between two points on the circumference is called a chord

  • The area formed between a chord and an arc is called a segment

  • A line which intersects the circumference at one point only, is called a tangent

• The ratio  is equal to 𝝅 (3.14159...)

• There are many properties relating to angles and other features of circles

  • These properties are sometimes known as circle theorems

  • You should be familiar with some of these from your National 4 Maths course

    • For example, the angle at the circumference in a semicircle is 90°

    • Or a tangent at a point on the circumference is perpendicular to a radius at that point

Circle Property: The perpendicular bisector of a chord passes through the centre

• If a line through the centre (such as a radius or diameter) goes through the midpoint of chord

  • it will bisect (cut in half) that chord at right angles to it

• To spot this circle property on a diagram

  • look for a radius and see if it intersects any chords

  • or look to see if you could draw a radius that bisects a chord

• If you need to explain this property in an exam you could use either phrase below:

  • A radius bisects a chord at right angles

  • The perpendicular bisector of a chord passes through the centre