Calculating outer corner radius for concentric rounded corners of a border

Question

I have rectangle with a border. The rectangle is 50x50 with a corner radius of 5.

When using the same corner radius for the border the result is:

But I actually need something like this:

How to calculate the border corner radius? Can this be calculated somehow with only the border width and corner radius?

Answer 1

In order to have both corner-curves concentric use

outerradius = cornerradius + borderwidth

This will get the straight parts start and end in parallel at the same (horizontal or vertical) position, i.e. the center of both quarter-circles is at the same point.