Circles: Arc Length
Master every arc length concept tested on the SAT — from basic formulas to advanced applications
SAT Math
Geometry
High-Yield Topic
1. What Is an Arc?
Key Definitions
| Term | Definition |
|---|---|
| Arc | A portion of a circle's circumference between two points. |
| Endpoints | The two points on the circle that define the arc. |
| Central Angle (θ) | The angle at the center whose sides pass through the arc's endpoints. The arc is "cut off" by this angle. |
| Minor Arc | Arc < half the circle; central angle < 180° |
| Major Arc | Arc > half the circle; central angle > 180° |
| Semicircle | Arc = half the circle; central angle = 180° |
Notation: Arc AB is written as ⌢AB. For a major arc, a third point is included (e.g., ⌢ACB) to avoid ambiguity.
Interactive visualization — available in the full lesson
⚠️ Critical Distinction: Arc measure is in degrees (or radians) — it equals the central angle. Arc length is in linear units (cm, m, inches) — it is the actual distance along the curve. The SAT loves testing whether you know the difference!
2. Central Angle & Arc Measure
360°
Full circle arc measure
Arc length = $2\pi r$
180°
Semicircle arc measure
Arc length = $\pi r$
90°
Quarter circle arc measure
Arc length = $\frac{\pi r}{2}$
Congruent arcs are arcs with equal measures in the same circle (or in congruent circles).