What is the probability that a random chord is longer than the radius?

What is the probability that a random chord is longer than the radius?

Approach: Assume random endpoints or random midpoint.

Depends on model. For random endpoints: chord length > radius when central angle > 60°, probability = 2/3. For random midpoint: probability = 3/4.

Follow-up: What is the expected length?

Key concepts: chord length, geometric probability, uniform distribution.