Circle Terminology
Year 9 📐 Geometry & Measures Chord, arc, sector, segment, tangent, circumference, area.
🔵 Parts of a Circle
Knowing the correct vocabulary is essential for all circle questions.
| Term | Definition |
|---|---|
| Radius ($r$) | Distance from centre to circumference |
| Diameter ($d$) | Distance across through the centre; $d = 2r$ |
| Chord | Line segment joining two points on the circumference |
| Arc | Part of the circumference |
| Sector | A "pie slice" — two radii and an arc |
| Segment | Region between a chord and an arc |
| Tangent | Line touching the circle at exactly one point |
📐 Arc Length and Sector Area
Calculate arc length or sector area using the angle at the centre.
⚡ Arc Length
$$\text{Arc length} = \frac{\theta}{360} \times 2\pi r$$⚡ Sector Area
$$\text{Sector area} = \frac{\theta}{360} \times \pi r^2$$Example: Sector: $r = 9$ cm, $\theta = 80°$. Area $= \frac{80}{360} \times \pi \times 81 = 18\pi \approx 56.5$ cm²
🔺 Tangent Properties
Two important tangent properties appear frequently in exam questions.
- A tangent is perpendicular to the radius at the point of contact.
- Two tangents from an external point are equal in length.
Example: From external point P, tangents touch a circle of radius 5 cm. If $OP = 13$ cm, then by Pythagoras: $PA = \sqrt{13^2 - 5^2} = \sqrt{144} = 12$ cm.
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Circle Terminology
🎬
Interactive demonstration available in the Calculator tab!
🔵 Circle Geometry Tool