Arc

What is an Arc?

An arc is one of the portions of a circle. An arc can be a portion of some other curved shapes like an ellipse but mostly refers to a circle. To avoid all the possible mistakes, it is also known as circular arc.

A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

Naming:

Arc

An Arc is named based on its endpoints. The red arc in the above figure, is called as arc AB or BA, since the order of points doesn’t matter. This can be expressed as the letter AB with a curved line above it, such as \(\widehat{AB}\) and read as “arc AB”.

Arc length:

The arc’s length is computed in distance units, such as centimeters. To indicate it, the arc is preceded by the lowercase letter L(for ‘length’). For instance, \(\widehat{lAB}\) = 7 inches is read as “the length of the arc AB is 7 inches”.

Arc

The arc can be measured in two ways.

  1. The angle of the arc.
  2. The length of the arc.

Angle Measure:

The angle that is created by the arc at the middle of the circle is nothing but the angle measure. It’s described by the letter m preceding the name. For instance, \(\widehat{mAB}\) = 600is read as “the arc AB has a measure of 60 degrees”.

Central angle in degrees

The formula to measure arc is:

Arc length = 2πr(c/360)

where,

C indicates the central angle of the arc in degrees

R indicates the radius of the arc 

Length of an Arc formula

When the central angle is in radians, the formula is expressed as:

Arc length = R C

Where,

C indicates the central angle of the arc in radians.

R indicates the radius of the arc.

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