The cumulative distribution function (CDF) for a uniform distribution on a circle is expressed in relation to the geometry of the circle, specifically as the fraction of the circle that lies below and to the left of a given point (x,y). The probability density function (PDF) is defined using the Dirac delta function, which complicates the integration process. To compute the CDF, one can consider the arc length of the circle contained within the specified quadrant defined by (x,y). Specific points like F(0,0) and F(1,0) yield values of 1/4 and 1/2, respectively, indicating their relative positions concerning the circle. Understanding the CDF involves determining the points on the circle that correspond to the given Cartesian coordinates and calculating the fraction of the circle they encompass.