I have a bounding box that is represented as a Cartesian starting point $(0,0)$ with a width and a height.
I have a circle with centre point that can be anywhere within the bounding box. The circumference of the circle is fixed.
When the circle intersects the edge of the bounding box an arc is formed. This new arc has to have a length equal to the circumference of the original circle.
The location of the centre of the circle is known, therefore the distance from the centre to the edge of the bounding box is known.
As you move closer to the edge of the bounding box, the radius of the circle must increase to keep the arc length the same.
The start and stop points of the arc are unknown as the radius is unknown.
This is where I'm stuck. Knowing only the distance from the bounding box and the fixed length of the arc how can I find the radius of the circle?
I have drawn an image to represent the question but I'm unable to post due to lack of reputation.
Any help on this will be greatly appreciated as I have spent many days trying to figure this out.
What I am trying to achieve is a radial menu with a fixed number of items (of a fixed size) that can be displayed around a centre point. The fixed length is a calculated length that all menu items can fit around.
I am implementing this in .net, but for the sake of this query it's purely a math question.
This has been moved from stack overflow.