Here's a problem I'm having that involves a square and a circle. The square ABCD is partially within the circle so that the side AB of the square is also a chord of the circle and the side DC is a tangent of the circle. Here's an illustration of the problem in case my description doesn't convey it clearly enough:

The circumference of the circle divides the sides AD and BC by a certain ratio which looking at the image might be 1 : 3. How do I determine for certain what this ratio is?