Circle vocabulary
OCR J560 expects fluent labelling of every standard part of a circle. Misreading "arc" for "chord" or "sector" for "segment" loses easy B1 marks across all six papers.
Core definitions
| Term | Meaning |
|---|---|
| Centre | Fixed point equidistant from every point on the circle. |
| Radius | Straight line from centre to circumference. (Plural: radii.) |
| Diameter | Chord through the centre. Length = 2 × radius. |
| Circumference | The perimeter (full distance round) of the circle. |
| Chord | Straight line joining two points on the circumference. |
| Arc | A portion of the circumference between two points. Minor arc is shorter, major arc is longer. |
| Tangent | A straight line touching the circle at exactly one point. |
| Secant | A straight line cutting the circle at two points (so contains a chord). |
| Sector | Region enclosed by two radii and the arc between them ("pizza slice"). |
| Segment | Region enclosed by a chord and the arc it cuts off. Minor (smaller) and major. |
Key properties
Tangent–radius: a tangent is perpendicular to the radius drawn to the point of contact. This single fact unlocks dozens of OCR Higher problems.
Two tangents from a point: equal in length. So if PA and PB are tangents from external point P, then PA = PB and triangle OAP is congruent to triangle OBP.
Arc length of a sector with angle θ° at the centre: L = (θ/360) × 2πr.
Sector area: A = (θ/360) × πr².
Segment area (minor) = sector area − triangle area = (θ/360)πr² − ½r²sin θ.
OCR mark scheme conventions
- Diagrams must be labelled correctly to earn B1; "the line" is not enough — write "tangent at A".
- For arc/sector calculations, leave answers in terms of π unless the question demands a decimal.
- "Use π = 3.14" overrides the default; otherwise use the calculator's π.
⚠Common mistakes
- Confusing arc (curve) with chord (straight line).
- Confusing sector (two radii + arc) with segment (chord + arc).
- Forgetting tangent ⊥ radius at the point of contact.
- Using degrees in the arc-length formula when the calculator is set to radians.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves