MathCirclesMedium frequency
SAT Math: Relate central angles to arcs (in degrees and radians)
15+ practice questions in Praczo
What you need to know
The concept, explained
- 1
A central angle is an angle whose vertex is at the center of the circle. The arc it intercepts has the same measure in degrees as the central angle.
- 2
Arc length = (central angle / 360°) · 2πr when angles are in degrees. In radians, arc length = rθ.
- 3
A full circle is 360° or 2π radians. Half of that (180° or π rad) corresponds to a semicircle.
- 4
Convert between degrees and radians using π rad = 180° (so 1° = π/180 rad).
Common mistakes
- ✗ Using degree measure where radians are required in the arc-length formula rθ.
- ✗ Forgetting to convert the central angle to the fraction of the full circle when computing arc length.
Try a sample question
SAT-style practice
A circle has radius 10. A central angle of 72° subtends an arc. What is the length of that arc?
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