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.

TermDefinition
Radius ($r$)Distance from centre to circumference
Diameter ($d$)Distance across through the centre; $d = 2r$
ChordLine segment joining two points on the circumference
ArcPart of the circumference
SectorA "pie slice" — two radii and an arc
SegmentRegion between a chord and an arc
TangentLine 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.
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🎬 Interactive Demonstration — Circle Terminology
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🧮 🔵 Circle Geometry Tool