In geometry, an arc represents a portion of a circle’s circumference. When an arc is larger than a semicircle (i.e., greater than 180 degrees), it is classified as a major arc. Its measure is determined by subtracting the measure of its corresponding minor arc from 360 degrees. For instance, if a minor arc subtends a central angle of 60 degrees, the related major arc measures 300 degrees (360 – 60 = 300). This value represents the proportion of the entire circle encompassed by the arc.
Understanding the measurement of these arcs is essential in various geometric calculations and applications. It allows for the accurate determination of lengths along circular paths, areas of circular sectors, and relationships between angles inscribed within circles. Historically, the study of circular arcs has been integral to fields such as astronomy, navigation, and engineering, providing the foundation for precise measurements and calculations in these disciplines. Its practical value extends to modern applications, including computer graphics, architecture, and mechanical design, where arcs are frequently employed to define curved shapes and trajectories.
