Circles
6 minQuiz at the end
Key Circle Vocabulary
- Centre: the middle point
- Radius (r): distance from centre to edge
- Diameter (d): distance across the circle through the centre; d = 2r
- Circumference: the perimeter (distance around) the circle
- Chord: a line segment joining two points on the circle
- Arc: part of the circumference
- Sector: a "pizza slice" (two radii + arc)
- Tangent: a line that touches the circle at exactly one point
Key Formulas
Circumference: C = Οd = 2Οr
Area: A = ΟrΒ²
Example: circle with radius 5cm:
- C = 2Ο(5) = 10Ο β 31.4cm
- A = Ο(5Β²) = 25Ο β 78.5cmΒ²
Sectors
Arc length = (ΞΈ/360) Γ 2Οr
Sector area = (ΞΈ/360) Γ ΟrΒ²
Circle Theorems
| Theorem | Rule |
|---|---|
| Angle in semicircle | Always 90Β° |
| Angles in same segment | Equal |
| Angle at centre | Twice angle at circumference |
| Opposite angles in cyclic quadrilateral | Sum to 180Β° |
| Tangent perpendicular to radius | Always 90Β° |
| Tangents from external point | Equal length |