A circle of radius r is a curve that consists of all points at distance r from the center of the circle.

A disk of radius r is the set of all points whose distance from its center is less than or equal to r.

Thus, a circle is the boundary of a disk.

 

Circles of radius 10 and 5. A random circle of radius 1, whose center is inside the larger circle, may or may not intersect the circle of radius 5. In the figure, the circle whose interior is shaded intersects the circle of radius 5. The other two circles of radius 1 do not intersect the circle of radius 5. (a). We generate a random circle of radius 1, whose center is uniformly distributed inside a disk of radius 10 centered at the origin; see figure above. Find the probability that the random circle intersects a circle of radius r = 5, also centered at the origin. (Give a numerical answer.) (b). Answer the same question as in Part (a) but for the case where r, instead of being 5, is the realized value of a random variable R that is uniformly distributed between 2 and 5. (Give a numerical answer.)