Educators have found that the concept of randomness is often misunderstood by students. Chance recently pointed out that students should be introduced to the concept of randomness through the use of simulations. In this article, we studied various aspects of the probability distribution off linear random path in a circle and introduce some related simulations to guide student exploration and discovery. Consider a random line segment that crosses a circle with a certain radius. Perhaps it can be considered to be a path that an airplane shows up and flies into a random direction in a monitor. What is the expected amount of flying distance through the monitor, and the expected variationulcorner Are we monitoring what we see scientificallyulcorner This article studies the probability distribution and some related aspects of a linear random path within a circular monitor. Some simulative activity is also introduced which can be used in a statistics or probability classes.