How to paint a circle with a random size on a random coordinate such that the circle is fully visible?

Code:

Random rand = new Random();
JPanel mainPanel;

int randomSize = 0; 
int randomPositionX = 0;
int randomPositionY = 0;

final static int FRAME_HEIGHT = 500;
final static int FRAME_WIDTH  = 500;

final static int TITLE_BAR    = 30 ;

final static int MAX_SIZE     = 100;
final static int MIN_SIZE     = 10 ;

/* All the below code is put into a method */

mainPanel = new JPanel(){   
    @Override
    public void paintComponent(Graphics g) {
        super.paintComponent(g);
        g.setColor(Color.RED);
        g.fillOval(randomPositionY, randomPositionX, randomSize, randomSize);
    }
};

do{
    randomSize = rand.nextInt(MAX_SIZE) + 1;
}while(randomSize < MIN_SIZE);

do{
    randomPositionX = rand.nextInt(FRAME_WIDTH);
    randomPositionY = rand.nextInt(FRAME_HEIGHT);
}while((randomPositionX + randomSize > FRAME_WIDTH) || (randomPositionY + randomSize > FRAME_HEIGHT - TITLE_BAR));

repaint();

What I want is the circle to have a random size such that it should have a minimum size of 10 and a maximum size of 100. The circle should also be painted in a random coordinate such that the circle is fully visible inside the JPanel mainPanel.

Note that mainPanel will be added to a JFrame whose size is set using setSize(FRAME_WIDTH, FRAME_HEIGHT);.

But the problem is that sometimes, a part of the circle is half outside and half inside the JPanel:

Where did I go wrong?