Drawing circles from array to a Form
The overall structure of your code looks good, but the readability is a tad poor. You should always strive to follow the Framework Design Guidelines. Use proper naming and add a few linebreaks.

Rather than using arrays, create a dedicated "Sprocket" class to hold the parsed input data.

Public Class Sprocket
    Public Property X As Integer
    Public Property Y As Integer
    Public Property R As Integer
End Class


Now, if you add the rest of the non-numeric characters to the separator list you could actually read and parse the file in two lines. (Though you ougth to use the line-continuation character for readability as seen at the bottom)

Dim numbers = File.ReadAllText("C:\Temp\gearinput.txt").Split($"{Environment.NewLine} ,)(".ToCharArray(), StringSplitOptions.RemoveEmptyEntries).Select(Function(n) Integer.Parse(n)).ToArray()
Dim sprockets = Enumerable.Range(0, (numbers.Length \ 3)).Select(Function(i) New Sprocket With {.X = numbers(((i * 3) + 0)), .Y = numbers(((i * 3) + 1)), .R = numbers(((i * 3) + 2))}).ToArray()






Sprocket.vb

Public Class Sprocket

    Public Property X As Integer
    Public Property Y As Integer
    Public Property R As Integer

    Public Overrides Function ToString() As String
        Return $"{{ X={Me.X}, Y={Me.Y}, R={Me.R} }}"
    End Function

End Class


Program.vb

Public Module Program

    &lt;STAThread&gt;
    Public Sub Main()

        'TODO: Read file
        Dim input = "(0, 0, 16),  (100, 0, 16),  (100, 100, 12),  (50, 50, 24),  (0, 100, 12)"

        Dim numbers = input _
            .Split($"{Environment.NewLine} ,)(".ToCharArray(), StringSplitOptions.RemoveEmptyEntries) _
            .Select(Function(n) Integer.Parse(n)) _
            .ToArray()

        Dim sprockets = Enumerable _
            .Range(0, (numbers.Length \ 3)) _
            .Select(Function(i) New Sprocket With
            {
                .X = numbers(((i * 3) + 0)),
                .Y = numbers(((i * 3) + 1)),
                .R = numbers(((i * 3) + 2))
            }) _
            .ToArray()

        Application.EnableVisualStyles()
        Application.SetCompatibleTextRenderingDefault(False)
        Application.Run(New Window(sprockets))

    End Sub

End Module


Window.vb    

Public Class Window
    Inherits Form

    Private ReadOnly sprockets As Sprocket()

    Public Sub New(sprockets As Sprocket())

        If (sprockets Is Nothing) Then
            Throw New ArgumentNullException(NameOf(sprockets))
        End If

        Me.sprockets = sprockets

        Me.SetStyle(ControlStyles.AllPaintingInWmPaint Or ControlStyles.UserPaint Or ControlStyles.OptimizedDoubleBuffer, True)

        Me.Text = "Sprockets"
        Me.AutoScaleMode = AutoScaleMode.Font
        Me.ClientSize = New Size(800, 450)

    End Sub

    Protected Overrides Sub OnPaint(e As PaintEventArgs)

        e.Graphics.Clear(Me.BackColor)
        e.Graphics.SmoothingMode = Drawing2D.SmoothingMode.HighQuality

        For Each sprocket In Me.sprockets

            Dim diameter = (sprocket.R * 2)
            Dim rect = New Rectangle(sprocket.X, sprocket.Y, diameter, diameter)

            e.Graphics.FillEllipse(Brushes.Black, rect)

        Next

    End Sub

End Class