Circle Sector and Segment

Circle Sector and Segment

Slices There are two main "slices" of a circle: ·         The "pizza" slice is called a Sector. ·         And the slice made by a chord is called a Segment.

SECTOR OF A CIRCLE

Common Sectors

The Quadrant and Semicircle are two special types of Sector:

Half a circle is 
a Semicircle.

Quarter of a circle is
a Quadrant.

Area of a Sector

A circle has an angle of 2π and an Area of:		πr2
A Sector with an angle of θ (instead of 2π) has an Area of:		(θ/2π) × πr2
Which can be simplified to:		(θ/2) × r2

Area of Sector = ½ × θ × r²   (when θ is in radians)

Area of Sector = ½ × (θ × π/180) × r²   (when θ is in degrees)

Arc Length By the same reasoning, the arc length (of a Sector or Segment) is: L = θ × r   (when θ is in radians) L = (θ × π/180) × r   (when θ is in degrees)

Area of Segment The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here). There is a lengthy reason, but the result is a slight modification of the Sector formula:
Area of Segment = ½ × (θ - sin θ) × r2   (when θ is in radians) Area of Segment = ½ × ( (θ × π/180) - sin θ) × r2   (when θ is in degrees)