I'm in a good mood today, so I'll give you ready-made (compilable) solution, if this isn't enough, then you need to go back to the books (you should anyway, most of stuff guys above are saying is in the documentation)
Qt Code: 
  1. // header
  2. #ifndef MAINWINDOW_H
  3. #define MAINWINDOW_H
  4.  
  5. #include <QtGui/QMainWindow>
  6.  
  7. class MainWindow : public QMainWindow
  8. {
  9.     Q_OBJECT
  10.  
  11. public:
  12.     MainWindow( QWidget* parent = 0 );
  13.  
  14. public slots:
  15.     void    redrawEllipse( void );
  16.  
  17. protected:
  18.     void    paintEvent( QPaintEvent* event );
  19.  
  20. private:
  21.     int radius;
  22. };
  23.  
  24. #endif // MAINWINDOW_H
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Qt Code: 
  1. // implementation
  2. #include "mainwindow.h"
  3.  
  4. #include <QPainter>
  5. #include <QTimer>
  6.  
  7. MainWindow::MainWindow( QWidget* p )
  8.     :
  10.     radius( 1 )
  11. {
  12.     QTimer* t = new QTimer( this );
  13.     connect( t, SIGNAL( timeout() ), this, SLOT( redrawEllipse() ) );
  14.     t->start( 10 );
  15. }
  16.  
  17. void    MainWindow::redrawEllipse( void )
  18. {
  19.     radius += 2;
  20.  
  21.     if( radius > qMin( this->width()/2, this->height()/2 ) )
  22.     {
  23.         radius = 1;
  24.     }
  25.  
  26.     this->update();
  27. }
  28.  
  29. void    MainWindow::paintEvent( QPaintEvent* e )
  30. {
  31.     Q_UNUSED( e );
  32.  
  33.     QPainter p( this );
  34.     p.drawEllipse( this->rect().center(), this->radius, this->radius );
  35. }
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