Arc (geometry)

• Circular arc of length b
• Chord of length l

If you put on a circle any two points fixed and connects them by stretching the center of the circle, so the two arms of the circular area, which are separated from each other by these routes, (also called circular sector ) sections of a circle represents a circular cutout is so to speak of two radii of a circle " cut out ". The belonging to a circle sector of the circle is referred to as a circular arc; the angle between the two radii referred to as center angle.

Calculation

The length b of a circular arc with the central angle α in degrees and the radius r can be calculated by the following formula:

The area of ​​the corresponding circle sector is calculated as follows:

Are you the center angle α in radians, so results in the following formulas:

It is striking that α = 360 ° and α = 2π, in fact, given the known formulas for circumference and area of ​​a circle by inserting the angle.

The chord of length l one gets via the following connection of the circular arc of radius r and b or directly from the central angle: