Introduction to Circles and Sectors
In this subtopic, we explore three key measurements related to circles: the circumference and arc length, and the area of sectors. These concepts appear frequently in IB exam questions — often combined — so it's important to understand both the formulas and when to apply them.
Recall the basic properties of a circle:
- Circumference:
- Area:
A sector is a 'pizza slice' of a circle — the region bounded by two radii and the arc between them. An arc is simply the curved portion of the circumference cut off by those two radii.
For IB Math AI SL, all angle calculations in this subtopic are done in degrees. You will not be required to use radian measure, but understanding the structure of the formulas helps you apply them confidently.
Key Definitions
A portion of the circumference of a circle, cut off by two radii. The arc is described as minor (less than half the circumference) or major (more than half) depending on the central angle.
The region of a circle enclosed by two radii and the arc between them. Like a slice of pizza or pie. The central angle is the angle at the centre between the two radii.
The angle formed at the centre of a circle between two radii. In this subtopic, is always measured in degrees.
Think of cutting a pizza. The crust you're eating is the arc, and the entire slice — crust, cheese, and all — is the sector. The angle at the pointy end is the central angle .