arc – part of a circumference of a circle

(pronounced arc)

To remember the meaning of arc, use the following mnemonic:

He sailed the ark (arc) across part of the circumference of the world (circle).

When you take any two points on a circle and connect them along the curved edge rather than with a straight line, that curved segment is an arc.

Arcs are typically measured by their length (the actual distance along the curve) or by their central angle (the angle formed at the centre by drawing lines to the arcs endpoints). A minor arc is less than half the circle's circumference, while a major arc is more than half.

Using the radius and the central angle, it is possible to work out arc length.

Example

Work out the length of the arc AB

Circumference`=2pir`

Therefore Circumference`=2pi times12` `cm`

                                             `=24pi` `cm`

Logic progresses as follows:

  `24pi=100%`of the circumference

`360^@=24pi` `cm`

  `60^@=x` `cm` 

 Answer: The arc is `x=4pi` `cm` long = 12.57cm