[Rachel Lim]

I'm happy to see these again!

I got (k+1)^2 / (4 * sqrt(k) * (k-1)), given k > 0 and the diameters != 0

My working is attached below. I mixed up the question, and the equation written is the ratio of base to hypotenuse instead of the other way around. It took me a while to realize some of the geometry the circles provide (and accept the fact that I'd need to use trig), so this is the simplest but not the first solution I found.

Edit: k > 1