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.