Calculating the Length of a Minor Arc | Formula and Example

Minor Arc

In geometry, a minor arc is a part of a circle that measures less than 180 degrees

In geometry, a minor arc is a part of a circle that measures less than 180 degrees. It is formed by drawing two radii (plural of radius) of the circle and the portion of the circumference between them. The length of a minor arc is proportional to the measure of its central angle, which is the angle formed by the radii.

To calculate the length of a minor arc, you can use the formula:

Length of minor arc = (measure of central angle / 360 degrees) x (circumference of the circle)

For example, let’s say you have a circle with a radius of 5 units and want to find the length of a minor arc formed by a central angle of 60 degrees.

First, calculate the circumference of the circle using the formula: Circumference = 2πr

Circumference = 2 x π x 5 = 10π units

Then, apply the formula for the length of a minor arc:

Length of minor arc = (60 degrees / 360 degrees) x (10π units) = (1/6) x 10π = (5/3)π units

So, the length of the minor arc is (5/3)π units or approximately 5.24 units (if we use an approximation of π as 3.14).

It’s important to note that the length of a minor arc is dependent on the measure of the central angle and the size of the circle. The larger the central angle, the longer the arc. Similarly, a larger circle will result in a longer arc for the same central angle.

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