Sheet № 216 · Foundation + Higher · AQA · Edexcel · OCR
Parts of a Circle –
Parts of a circle is a core GCSE Maths vocabulary topic that underpins many other areas — from area and circumference calculations to circle theorems. You must know the precise definitions of each part and be able to identify them on a diagram. This guide defines every term you need, shows how they relate to each other, and provides worke
§Key definitions
Question:
A circle has a radius of 8 cm. Find the diameter, circumference, and area.
Answer:
Diameter = 16 cm, circumference = 50.3 cm, area = 201.1 cm².
Q1 (Foundation):
A circle has diameter 14 cm. Find the radius and circumference.
Q2 (Foundation):
Name the part of a circle that is the region between a chord and the arc.
Q3 (Higher):
A chord of length 24 cm is drawn in a circle of radius 13 cm. Find the perpendicular distance from the centre to the chord.
§Formulas to memorise
Circumference = 2πr = πd
Area of a circle = πr²
Diameter = 2 × radius
Centre: — The fixed point in the middle of the circle.
Radius (r): — The distance from the centre to any point on the circumference. Plural: radii.
Diameter (d): — A straight line passing through the centre, connecting two points on the circumference. Always d = 2r.
Circumference: — The perimeter (total distance around) the circle.
Chord: — A straight line connecting any two points on the circumference. A diameter is a special chord that passes through the centre.
Tangent: — A straight line that touches the circumference at exactly one point. It is perpendicular to the radius at the point of contact.
Arc: — A portion of the circumference — a curved section between two points.
Worked example
A circle has a radius of 8 cm. Find the diameter, circumference, and area.
Working:
⚠ Common mistakes
- ✗Confusing radius and diameter. The diameter is twice the radius. Always check which one the question gives you before substituting into a formula.
- ✗Confusing sector and segment. A sector is bounded by two radii and an arc (pizza slice shape). A segment is bounded by a chord and an arc.
- ✗Forgetting the tangent-radius relationship. A tangent is always perpendicular to the radius at the point of contact — this is a key fact for circle theorem questions.
✦ Exam tips
- →Learn all the vocabulary precisely — exam questions may simply ask you to label or identify parts of a circle for straightforward marks.
- →Remember that "chord," "tangent," "arc," "sector," and "segment" appear in circle theorem questions — knowing the definitions helps you understand the theorems.
- →When a question mentions a tangent, immediately think "perpendicular to radius" — this usually sets up a right-angled triangle.
- →Minor arc/sector/segment means the smaller one; major means the larger one.