Bertrand's paradox java simulation

I found an interest math problem Bertrand's paradox. This problem was originally posed by Joseph Bertrand in his work.

The Problem

Determine the probability that a random chord of a circle of unit radius has a length greater than the square root of 3, the side of an inscribed equilateral triangle.

Experiment simulation

I've modeled this problem with 3 java classes (Circle, Point, Main). The Main class does the experiment with other 2 classes. The main problem in this paradox is the random chord definition. What do we mean under random chord? I try to implement the problem in the way that I select both chords of circle object randomly.

My algorithm for generating 2 random chord

(we have a circle)

1. Select a random coord (x,y) anywhere (2 random real numbers)
2. This define a direction vector. Scale it to radius length.
3. Shift this chord, if the center of circle is not (0,0).
4. Now the first chord is done.
5. Repeat 1-3. steps for generate second chord of circle.
6. Evaluate two point distance and compare it with the side of triangle.

You can set the number of experiments a command line parameter.

My result

My result was 33.33% or 1/3. I've executed this simulation for 10,000,000 experiments. The result was 33.333%. You can try it also and view the source and I welcome any comment for this post.

Download

You can download the experiment simulation program. Feel free to edit, copy or distribute the code. The .zip file is included the sources (Circle.java, Point.java, Main.java) and the executable .jar version:
bertrand_paradox.zip [6.89 KB]