Arc Length

• Arc length represents the distance along part of the circle’s edge.
• Formula (degrees): \( \text{Arc Length} = \frac{\theta}{360} \times 2\pi r \)
• Formula (radians): \( \text{Arc Length} = r\theta \)

Tangent Lines

• A tangent line touches the circle at exactly one point.
• It is always perpendicular to the radius at the point of contact.
• Often tested in problems involving right triangles formed by radii and tangents.

Using Arc Length and Radius

• To find the fraction of the circumference represented by an arc:
• Fraction = Arc Length / Circumference
• Circumference = 2πr
• Then use the fraction to find angle measures or areas.
• Can also reverse-engineer the angle or radius if arc length and one other value are known.