Geometric probability of intersection of a square and a circle

In the unitary square we choose a point (X,Y) with iid coordinates U[0,1] and a radius R, independent of (X,Y) and U[0,1], and we draw the circle of radius R with center (X,Y). Find the probability that this circle intersects the circumference of the unit square.

In the unitary square we choose a point (X,Y) with iid coordinates U[0,1] and a radius R, independent of (X,Y) and U[0,1], and we draw the circle of radius R with center (X,Y). Find the probability that this circle intersects the circumference of the unit square.