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 worked examples and practice questions.

What Are the Parts of a Circle?

A circle is the set of all points that are the same distance from a fixed centre point. The key parts are:

• 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.
• Sector: The region enclosed by two radii and an arc — shaped like a pizza slice.
• Segment: The region between a chord and the arc it cuts off.

Key Formulas

Step-by-Step Method

Identifying Parts on a Diagram

1. Locate the centre — all radii start here.
2. Any line from the centre to the edge is a radius.
3. A line through the centre from edge to edge is a diameter.
4. A line from edge to edge not through the centre is a chord.
5. A line touching the circle at one point is a tangent.
6. A curved portion of the edge is an arc.
7. A region bounded by two radii and an arc is a sector.
8. A region between a chord and its arc is a segment.

Using the Terms in Calculations

1. Identify which part of the circle the question refers to.
2. Select the appropriate formula (circumference, area, arc length, sector area).
3. Substitute the known values and solve.

Worked Example 1 — Foundation Level

Question: A circle has a radius of 8 cm. Find the diameter, circumference, and area.

Working:

Step 1 — Diameter = 2 × 8 = 16 cm.

Step 2 — Circumference = 2 × π × 8 = 16π ≈ 50.3 cm (1 d.p.).

Step 3 — Area = π × 8² = 64π ≈ 201.1 cm² (1 d.p.).

Answer: Diameter = 16 cm, circumference = 50.3 cm, area = 201.1 cm².

Worked Example 2 — Higher Level

Question: A chord AB divides a circle of radius 10 cm into two segments. The chord is 12 cm long. Find the distance from the centre to the chord.

Working:

Step 1 — Draw a perpendicular from the centre O to the midpoint M of chord AB. This perpendicular bisects the chord.

Step 2 — AM = 12 ÷ 2 = 6 cm.

Step 3 — Triangle OMA is right-angled with OA = 10 (radius) and AM = 6.

Step 4 — OM = √(10² − 6²) = √(100 − 36) = √64 = 8 cm.

Answer: The distance from the centre to the chord is 8 cm.

Worked Example 3 — Exam Style

Question: A tangent to a circle meets a radius at point P on the circumference. The radius OP = 5 cm and the tangent extends to point T where OT = 13 cm. Find the length of the tangent PT.

Working:

Step 1 — A tangent is perpendicular to the radius at the point of contact, so angle OPT = 90°.

Step 2 — Triangle OPT is right-angled. Using Pythagoras: PT² = OT² − OP².

Step 3 — PT² = 13² − 5² = 169 − 25 = 144.

Step 4 — PT = √144 = 12 cm.

Answer: The tangent length PT = 12 cm.

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.

Practice Questions

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.

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Related Topics

• Circle Theorems — angle rules involving chords, tangents, and arcs.
• Arc Length and Sector Area — calculating arc lengths and sector areas.
• Area of a Sector and Segment — finding segment areas.

Summary

Parts of a circle is essential vocabulary for GCSE Maths. You must know the definitions of radius, diameter, chord, tangent, arc, sector, and segment, and be able to identify each on a diagram. The diameter is always twice the radius. A tangent is perpendicular to the radius at the point of contact. A sector is like a pizza slice (two radii plus an arc), while a segment is the region between a chord and an arc. Mastering this vocabulary is the foundation for circle calculations and circle theorems.