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How to calculate the minor ARC of a circle

Updated August 03, 2018

A radius is a line drawn from the centre of the circle to its edge. When you draw two radii in a circle, you divide the circumference of the circle into two arcs: The major arc, which is the larger arc, and the minor arc, which is the smaller arc. If you know the measure of the major arc, you can find the minor arc's measure. However, to find the length of the minor arc, you must also know the circumference.

Subtract the major arc's angle measure from 360 to find the minor arc's measure. For example, if the major arc measures 288 degrees, subtract 288 from 360 to find that the minor arc measures 72 degrees.

Divide the minor arc's measure by 360 to find the portion of the circumference the minor arc comprises. In this example, divide 72 by 360 to get 0.2.

Multiply the portion of the circumference the minor arc comprises by the circumference of the circle to calculate the length of the minor arc. For example, if the circumference in this example equals 11 inches, multiply 11 by 0.2 to find that the minor arc measures 2.2 inches.

Tip

If you do not know the circumference, multiply the radius by two by 3.14. For example, a circle with a radius of 7 would have a circumference of 43.96.

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