Suppose I have a 20 X 30 rectangle R with an inscribed circle C of diameter 20 (touching 3 edges). What is the maximum diameter of a circle that can be inscribed in $R\setminus C$?
Clearly I can inscribe a diameter 10 circle, but clearly one can do better. What is the max?
Is there a formula for the general case of R a rectangle 1xL and C a circle of diameter 1? (Here I suppose $L\geq 1$)