Tangent of Uniform Distribution has Standard Cauchy Distribution/Examples

Examples of Use of Tangent of Uniform Distribution has Standard Cauchy Distribution

Radiation Particles

Let particles be emitted from a source of radiation $S$ in a plane in random (equally likely) directions.

Let these particles travel in a straight line to a plane collector some distance from $A$.

Then the distribution of the points of impact of the particles on the collector has a standard Cauchy distribution.