Question 321369
The area of the entire circle is {{{pi*r^2}}}.

In order to be closer to the center than the boundary, the point will have to fall past the halfway point toward the center. 

The circle that lies inside the larger circle has radius r/2.

Its area is {{{pi*(r/2)^2}}}

So, we have {{{(pi*(r/2)^2)/(pi*r^2)=1/4}}}