Circular Measure

The circumference of a circle is given byorwhereis the radius andis the diameter. The area of a circle is

We also need formulae for the length of an arc of a circle and the area of a sector of a circle.

These can be easily found by considering fractions of circles.

A circular arc subtends an angle at the centre of a circle. The length of the arc is just the angle subtended as a fraction oftimes the circumference:

The perimeter of the sector is then found by adding twice the radius.

The area of a sector is just the area of the circle times the angle subtended by the arc forming the sector divided by

The area formed by the triangle formed by two radii and a chord is

The area formed by the difference between a sector and a segment is given by subtracting the area of one from the other.

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