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The measurement of a minor arc, also known as the arc length, is an important concept in geometry and trigonometry. An arc is a portion of a circle, and its length is proportional to the angle subtended by the arc at the center of the circle. In this article, we will discuss the definition of a minor arc, how to measure it, and some important properties of minor arcs.

A minor arc is a portion of a circle that is smaller than a semicircle, which is half of the circle. In other words, a minor arc is any arc that is less than 180 degrees. The other type of arc is a major arc, which is larger than a semicircle and has a measure greater than 180 degrees.

To understand the concept of minor arcs, it is important to first understand some basic terms related to circles. A circle is a closed shape in which all points on the boundary are equidistant from the center. The diameter of a circle is a line segment that passes through the center of the circle and has endpoints on the boundary of the circle. The radius of a circle is a line segment that connects the center of the circle to any point on the boundary of the circle. The circumference of a circle is the distance around the boundary of the circle.

The measure of an arc is the degree measure of the central angle that subtends the arc at the center of the circle. In other words, the measure of an arc is the amount of rotation needed to sweep out the arc from its starting point to its endpoint. The measure of an arc is always given in degrees or radians.

To measure a minor arc, we first need to determine the measure of the central angle that subtends the arc at the center of the circle. The measure of the central angle can be found using the formula:

θ = (l/r) * (180/π)

where θ is the measure of the central angle in degrees, l is the length of the arc, r is the radius of the circle, and π is the mathematical constant pi, which is approximately equal to 3.14159.

Once we have determined the measure of the central angle, we can use this measure to find the measure of the minor arc. The measure of the minor arc is simply the same as the measure of the central angle. For example, if the central angle has a measure of 45 degrees, then the minor arc has a measure of 45 degrees as well.

Minor arcs have several important properties that are useful in geometry and trigonometry. Some of these properties are:

1.The length of a minor arc is proportional to the measure of the central angle that subtends it. This means that if two central angles have measures in the ratio a:b, then the lengths of the arcs that they subtend are also in the same ratio a:b.

2.The length of a minor arc is also proportional to the radius of the circle. This means that if two circles have radii in the ratio a:b, then the lengths of the arcs that they subtend are also in the same ratio a:b.

3.The sum of the measures of two minor arcs that share an endpoint is equal to the measure of the arc that spans the two arcs. For example, if arc AB has a measure of 30 degrees and arc BC has a measure of 60 degrees, then the measure of arc AC is 90 degrees, which is the sum of the measures of arcs AB and BC.

4.The length of a minor arc is equal to the product of the radius and the measure of the central angle, divided by 360. This means that if we know the radius.

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