Get the box with the radius corners put 2 Guide Lines on each edge of the box and draw a circle (starting origin for the circle is the intersecting Guide Lines) holding down the Ctrl Key until you circle matches the radius Corner. See Below.

Ok - here we go - hopefully this will post this time as I have tried to post this 5 times already...

A radius is half the diameter of a circle - so a 12" circle = 6" radius

So given that .... Drop a guideline @ the top & side or side & bottom of your object

Draw a circle - then select your circle & the object w/ the radius corner - hot key L & T for top left - or R & T for top right - or L & B for bottom left - or - R & B for bottom right / when your circle is in the correct corner - uniformally increase the size of your circle till it matches your corner - once your cicle matches look & see what the size is of your circle - then divide by "2" & you will have the radius of your corner

I think he was hoping some of us have already researched the solution using a macro. Personally, I don't see a macro making your solution happen faster/easier. You could simply use the dimension tool to measure from quadrant to the horizontal or vertical outer edge of the curve given that your radius is still true. Does that make sense?