Get radius of circle, when know height and width of part of including square

Question

Know width and height of square's part, which include circle. How I can get radius of that circle?

UPDATE: How to get radius of LARGEST circle, part of which could be placed inside known rectangle

Answer 1

The answer is

R = width/2 + height^2/(8*width)

Find the correct triangle and the problem becomes trivial.

You have two equations.

height/2 = R*SIN(Φ)
R = width + R*COS(Φ)

that are solved for R and Φ.