User Control with button and button events

public class CustomPictureBox : PictureBox
{
    bool hovered = false;
    Button btnClear;

    public CustomPictureBox()
    {
        this.MouseEnter += new EventHandler(CustomPictureBox_MouseEnter);
        this.MouseLeave += new EventHandler(CustomPictureBox_MouseLeave);

        btnClear = new Button();
        btnClear.Font = new System.Drawing.Font("Microsoft Sans Serif", 8.25F, System.Drawing.FontStyle.Bold, System.Drawing.GraphicsUnit.Point, ((byte)(0)));
        btnClear.BackColor = System.Drawing.Color.White;
        btnClear.Width = 20;
        btnClear.Height = 20;
        btnClear.Location = new Point(this.Width - btnClear.Width + 1, -1);
        btnClear.Visible = false;
        btnClear.Text = "X";
        this.Controls.Add(btnClear);
    }

    void CustomPictureBox_MouseLeave(object sender, EventArgs e)
    {
        Invalidate();
        hovered = false;
        btnClear.Visible = false;
    }

    void CustomPictureBox_MouseEnter(object sender, EventArgs e)
    {
        Invalidate();
        hovered = true;
        this.Cursor = System.Windows.Forms.Cursors.Hand;
        btnClear.Visible = true;
    }

    protected override void OnPaint(PaintEventArgs e)
    {
        //base.OnPaint(e);
        this.BorderStyle = System.Windows.Forms.BorderStyle.None;

        if (hovered)
        {
            Pen pen = new Pen(Color.DarkGray, 2);
            pen.Alignment = System.Drawing.Drawing2D.PenAlignment.Inset;
            pen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dash;
            Rectangle rectangle = new Rectangle(0, 0, this.Width, this.Height);
            e.Graphics.DrawRectangle(pen, rectangle);
        }
        else if (!hovered)
        {
            Pen pen = new Pen(Color.Gray, 1);
            pen.Alignment = System.Drawing.Drawing2D.PenAlignment.Inset;
            pen.DashStyle = System.Drawing.Drawing2D.DashStyle.Dot;
            Rectangle rectangle = new Rectangle(0, 0, this.Width -1, this.Height -1);
            e.Graphics.DrawRectangle(pen, rectangle);
        }
    }
}