Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Mensuration
Circles, Arcs and Sectors
What is Circles, Arcs and Sectors?
A circle of radius r has circumference 2 pi r, equal to pi d for diameter d, and area pi r squared. An arc is a part of the circumference and a sector is the region enclosed by an arc and the two radii at its ends. For a central angle theta measured in degrees, both are the same fraction theta over 360 of the whole circle, so the arc length is theta over 360 times 2 pi r and the sector area is theta over 360 times pi r squared. The smaller region is the minor sector and the larger is the major sector, whose angle is 360 minus theta. The perimeter of a sector is its arc length plus two radii. A segment is the region between a chord and its arc, and its area is found as the area of the sector minus the area of the triangle formed by the two radii and the chord.
This definition is part of the Mensuration chapter in Cambridge O Level Mathematics (Syllabus D).