Major arc

Definition

A major arc is a portion of a circle that is larger than a semicircle, defined by two endpoints on the circle and covering the longer path between those points. It represents the largest section of the circle that connects the two endpoints, and its measure is greater than 180 degrees. Understanding major arcs is essential for comprehending the relationships between different parts of circles, especially when dealing with angles, chords, and their properties.

5 Must Know Facts For Your Next Test

1. The measure of a major arc can be calculated as 360 degrees minus the measure of its corresponding minor arc.
2. In any circle, there are always two arcs (major and minor) defined by any two points on the circumference.
3. When naming a major arc, the longer arc is usually denoted with three points, where the first and last points are the endpoints and the middle point indicates a location along the arc.
4. A major arc can be visualized as encompassing more than half of the total circle's circumference.
5. When calculating angles associated with arcs, major arcs often require additional considerations compared to minor arcs due to their larger measurements.

Review Questions

• How does a major arc differ from a minor arc in terms of measurement and representation on a circle?
  • A major arc is defined as an arc that measures more than 180 degrees, while a minor arc measures less than 180 degrees. When representing these arcs on a circle, a major arc covers the longer path between two endpoints, often requiring three points for proper notation. This distinction in measurement impacts various calculations related to angles and other properties in geometry.
• What is the relationship between central angles and major arcs in terms of their measures?
  • The measure of a central angle corresponds directly to the measure of its associated minor arc. Since a major arc is defined as the longer arc between two endpoints on a circle, its measure can be derived by subtracting the measure of the minor arc from 360 degrees. This relationship is key in understanding how angles relate to different parts of circles and helps in various geometric calculations involving arcs.
• Evaluate how understanding major arcs contributes to solving complex problems involving circles and their properties.
  • Understanding major arcs is crucial for tackling complex problems in geometry as it enables one to recognize and differentiate between arcs based on their measures. For instance, when working with inscribed angles or determining distances along circular paths, knowing how to calculate and visualize both major and minor arcs allows for more comprehensive problem-solving strategies. Additionally, this knowledge aids in understanding relationships between chords, central angles, and sectors, which are all integral components in circular geometry.

Related terms

minor arc:

A minor arc is the shorter path between two endpoints on a circle, measuring less than 180 degrees.

chord: A chord is a straight line segment whose endpoints lie on the circle, which helps to define both major and minor arcs.

central angle:

A central angle is formed by two radii of the circle, with its vertex at the center of the circle, and it directly relates to the measures of both major and minor arcs.