Definitions [2]
Definition: Sector of a Circle
Sector of a circle
Region enclosed by two radii and the corresponding arc.
Minor sector
Sector with angle < 180°.
Major sector
Sector with angle > 180°.
Angle of major sector = 360° − angle of minor sector.
Definition: Segment of a Circle
Segment of a circle
Region enclosed by a chord and the corresponding arc.
Minor segment
A smaller region formed by the chord.
Major segment
The remaining larger region of the circle.
Formulae [3]
Formula: Area of a Sector
\[\text{Area of sector}=\frac{\theta}{360}\times\pi r^2\]
Formula: Length of an Arc
\[\text{Length of arc}=\frac{\theta}{360}\times2\pi r\]
Formula: Area of a Segment
Area of minor segment = Area of sector − Area of triangle
\[A(\text{minor segment})=\frac{\theta}{360}\pi r^2-\frac{1}{2}r^2\sin\theta\]
That is,
A(major segment) = πr2 − A(minor segment)
