Striking a random chord

Calculus Level 3

Two points are chosen uniformly at random on the circumference of a circle with radius 100.

What is the expected value for the distance between them?

Round your answer to the nearest integer.

1 solution

Geoff Pilling
Jul 5, 2016

You can calculate this as follows:

$100\frac{\int_{0}^{2\pi } 2\sin (\theta/2) d\theta}{2\pi} = 100\frac{8}{2\pi} \approx \boxed{127}$