Circle parts and definitions
This topic underpins the circle theorems (G10) and the geometry needed for arc/sector calculations. Edexcel includes the part-naming on Foundation and the calculation work on both tiers.
📖Definition— Definitions (memorise the wording)
- Centre — the fixed central point.
- Radius — a line from the centre to the circumference.
- Diameter — a chord passing through the centre. Length = 2 × radius.
- Chord — a straight line joining two points on the circumference.
- Circumference — the perimeter of the circle.
- Arc — a section of the circumference. Minor arc < semicircle; major arc > semicircle.
- Sector — a "pizza slice" region bounded by two radii and an arc.
- Segment — a region bounded by a chord and an arc. Minor segment is the smaller piece.
- Tangent — a straight line that touches the circle at exactly one point.
Key tangent property
A tangent is perpendicular to the radius drawn to the point of contact. This is one of the most-tested facts on Edexcel Paper 2H.
Arc length and sector area (formulas appear on the Edexcel formula sheet from 2025)
For angle θ at the centre (in degrees):
- Arc length = (θ/360) × 2πr
- Sector area = (θ/360) × πr²
Segment area (Higher only)
Segment area = sector area − area of the triangle formed by the two radii. Triangle area = (1/2) r² sin(θ).
So: segment area = (θ/360) × πr² − (1/2) r² sin(θ).
Circumference and area of the whole circle
- Circumference C = 2πr = πd.
- Area A = πr².
Common Edexcel exam tip
For a "leave your answer in terms of π" question, do NOT substitute π = 3.142. Keep the answer exact (e.g. 36π cm²). Substituting π loses A1.
⚠Common mistakes— Common errors
- Confusing chord and arc.
- Using diameter when radius is needed in πr² (a typical 2-mark error).
- Forgetting to subtract the triangle when finding a segment.
AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves