The Bullseye applet was so convoluted because it is relatively hard to center concentric rectangles inside another rectangle. On the other hand if you think of circles as being defined by their center point and a radius, it's not particularly difficult to draw concentric circles. Just keep the center point the same and draw circles with progressively larger radii. Write a CircleToRect method with the following signature
which takes as its arguments a java.awt.Point and a radius and returns a java.awt.Rectangle. Before beginning you should review the documentation for points and rectangles at http://www.javasoft.com/JDK-1.0/api/java.awt.Rectangle.html and http://www.javasoft.com/JDK-1.0/api/java.awt.Point.html.
public Rectangle CircleToRect(Point p, int radius)