I am trying to set up some simple 2D shapes which can be dragged about the window using the mouse. I want the shapes to register a collision when I drag one into another. I have an interface.
interface ICollidable
{
    bool CollidedWith(Shape other);
}
I then have an abstract class Shape that implements the above interface.
abstract class Shape : ICollidable
{
    protected bool IsPicked { private set; get; }
    protected Form1 Form { private set; get; }
    protected int X { set; get; } // Usually top left X, Y corner point
    protected int Y { set; get; } // Used for drawing using the Graphics object
    protected int CenterX { set; get; } // The center X point of the shape
    protected int CenterY { set; get; } // The center X point of the shape
    public Shape(Form1 f, int x, int y)
    {
        Form = f;
        X = x; Y = y;
        Form.MouseDown += new MouseEventHandler(form_MouseDown);
        Form.MouseMove += new MouseEventHandler(Form_MouseMove);
        Form.MouseUp += new MouseEventHandler(Form_MouseUp);
    }
    void Form_MouseMove(object sender, MouseEventArgs e)
    {
        if(IsPicked)
            Update(e.Location);
    }
    void Form_MouseUp(object sender, MouseEventArgs e)
    {
        IsPicked = false;
    }
    void form_MouseDown(object sender, MouseEventArgs e)
    {
        if (MouseInside(e.Location))
            IsPicked = true;
    }
    protected abstract bool MouseInside(Point point);
    protected abstract void Update(Point point);
    public abstract void Draw(Graphics g);
    public abstract bool CollidedWith(Shape other);
}
I then have ten concrete classes Circle, Square, Rectangle etc that extend the Shape class and implement the abstract methods. What I would like to do is come up with some oop clean and elegant way to do the collosion detection instead having a large block of if statements in the CollidedWith method such is
public bool CollidedWith(Shape other)
{
    if(other is Square)
    {
        // Code to detect shape against a square
    }
    else if(other is Triangle)
    {
        // Code to detect shape against a triangle
    }
    else if(other is Circle)
    {
        // Code to detect shape against a circle
    }
    ...   // Lots more if statements
}
Has anyone any ideas. It's a problem I've thought about before but am only putting into practice now.