Major Arc
High School
Definition
In situations where you have two arcs in a circle, the larger arc is referred to as the major arc. It is an arc that measures to or is greater than 180 degrees, which is also π in radians. Summing up the major arc and the minor arc (the arc that is smaller) gives you 360 degrees or 2π radians.
Worked examples
\(\)Arc \( ACB = 210^\circ\)
Since 210° exceeds 180°, arc ACB is the major arc; the matching minor arc AB measures 150°.
\(\)Major arc \( = \frac{5\pi}{3} \) rad\(\)
In radians, any arc measuring π or more is a major arc; this one is greater than π.
\(\)Major arc \( + \)Minor arc \( = 360^\circ\)
The two arcs between any pair of points on a circle always add to a full rotation.
Common mistakes
- \(\)Arc \( = 170^\circ \) is a major arc\(\) → \(170^\circ < 180^\circ \) so it is a minor arc\(\) A major arc must be at least 180°; anything less is minor.
- \(\)Major arc \( = 180^\circ\) → \(\)Major arc \( \ge 180^\circ\) Exactly 180° (a semicircle) is the boundary; some definitions call it major, others neither—check context.
- Using two letters (e.g., \(\)arc \( AB\)) to name the major arc → Use three letters (e.g., \(\)arc \( ACB\)) to specify which of the two arcs Two points create two arcs; three letters clarify you mean the longer path.
Where you'll use it next
Major arcs appear when finding arc length and sector area in geometry, analyzing circular motion in physics, and solving problems involving inscribed angles and circle theorems in advanced geometry and trigonometry.
Found in 1 StudyPug lesson
Mastering Arcs of a Circle: From Basic Concepts to Advanced Applications
10th Grade10thGeometry
Dive into the world of circular arcs! Learn to calculate arc lengths, understand different types, and explore real-world applications. Boost your geometry skills with our comprehensive guide.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026