Arc
In geometry, an arc is a curved segment of a circle
In geometry, an arc is a curved segment of a circle. It is typically defined by two endpoints and the points on the circle between these endpoints.
Arcs can be classified by their measures, which are typically given in degrees or radians. The measure of an arc is defined as the central angle that is subtended by the arc. In other words, it is the angle formed at the center of the circle between the two radii that connect the center to the endpoints of the arc.
To calculate the measure of an arc, you can use the following formulas:
1. If the angle measure is given in degrees:
Measure of the arc = (Angle measure / 360) * circumference of the circle
2. If the angle measure is given in radians:
Measure of the arc = Angle measure * radius of the circle
Note that the circumference of a circle is given by the formula 2 * π * radius, where π is approximately equal to 3.14159.
Once you have the measure of an arc, you can use it to calculate other properties, such as the length of the arc. The length of an arc is a portion of the circumference of the circle and can be calculated using the formula:
Length of the arc = (Measure of the arc / 360) * circumference of the circle
Remember to use radians instead of degrees if the angle measure is given in radians.
In summary, an arc is a curved segment of a circle defined by two endpoints and the points on the circle between them. The measure of an arc is the central angle it subtends, and it can be used to calculate the length of the arc.
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