The Resize event handler calls the form's Invalidate method. That generates a Paint event for the form's client area so the Paint event handler calls DrawCircle.

Subroutine DrawCircle clears the form (see what happens if you comment out that line) and then uses the Graphics object it was passed to draw a circle. It also draws an X on the form so it's easy to see that the circle is centered.

Private Sub Form1_Paint(ByVal sender As Object, ByVal e As _
    System.Windows.Forms.PaintEventArgs) Handles _
    MyBase.Paint
    DrawCircle(e.Graphics)
End Sub

Private Sub Form1_Resize(ByVal sender As Object, ByVal e As _
    System.EventArgs) Handles MyBase.Resize
    Me.Invalidate()
End Sub

Private Sub DrawCircle(ByVal gr As Graphics)
    Const RADIUS As Integer = 20
    Dim x As Integer = Me.ClientSize.Width \ 2 - RADIUS
    Dim y As Integer = Me.ClientSize.Height \ 2 - RADIUS
    gr.Clear(Me.BackColor)
    gr.DrawArc(Pens.Blue, x, y, 2 * RADIUS, 2 * RADIUS, 0, _
        360)
    gr.DrawLine(Pens.Red, 0, 0, Me.ClientSize.Width, _
        Me.ClientSize.Height)
    gr.DrawLine(Pens.Red, 0, Me.ClientSize.Height, _
        Me.ClientSize.Width, 0)
End Sub