What is the difference between chord length and arc length?

The **difference between chord length and arc length** lies in their definitions and geometric representations on a circle:

1. **Chord Length**:
- A chord is a straight line segment connecting two points on the circumference of a circle.
- The length of the chord is the straight-line distance between these two points.
- It does not follow the curve of the circle; instead, it is a direct line segment.

2. **Arc Length**:
- An arc is the curved portion of the circle's circumference between two points.
- The arc length is the distance measured along this curved path.
- It represents the actual length of the curved segment of the circle's circumference between two points.

### Key Difference:
- **Chord length** is a straight-line measurement between two points, while **arc length** measures the curved distance along the circle's circumference between the same two points.

### Example for Clarity:
Suppose we have two points A and B on a circle:
- The chord is the straight-line segment AB.
- The arc is the curved portion of the circle's circumference between A and B.

If the circle's radius is r and the angle subtended by the arc at the center is θ (in radians):
- **Chord Length** = \( 2r \sin(\theta/2) \)
- **Arc Length** = \( r \theta \)

These formulas further illustrate that the arc length will always be greater than or equal to the chord length (equality holds only when θ = 0, meaning A and B coincide).