Circles Kickoff Equal distance, perfect shape.

Arc & Chord

Circle showing a red arc and a black chord

Spot the Difference

Arc AB is the curved part of the circle between points A and B. Chord AB is the straight line segment joining the same two points.

Key Points:

  • Curved outline = Arc
  • Straight segment = Chord
  • Arc is usually longer than its chord

Arc Length

\[ L = 2\pi r \left( \frac{\theta}{360} \right) \]

Use when \( \theta \) is measured in degrees.

Variable Definitions

L arc length
r radius of the circle
θ central angle (degrees)

Applications

Measuring road bends

Engineers find curved road length to set safe speed limits.

Designing curved rail tracks

Determines rail length needed for a smooth train turn.

Circle Essentials

A circle: all points the same distance from the centre.

Arc: a portion of the circle’s boundary.

Chord: straight line joining any two points on the circle.

Arc length formula \(L = 2\pi r \times \frac{\theta}{360^\circ}\).

Arc length grows proportionally with radius \(r\) or angle \(\theta\).

Next Steps

Try solving two practice problems on arc length in your workbook.

Thank You!

Great job! You can now recall circle terms and the arc length formula.