



 
Hi Meg. We can draw this situation using a simpler twodimensional geometric sketch:
Thus, we are trying to obtain an expression for the length of the green segment in terms of the known blue (R) and red (r) segments. The black lengths are unknown at this time. First, I hope you recognize that the three triangles AED, ACF and ABH are all similar triangles (they are all right triangles sharing an angle). Thus, the ratios of their sides is common.
Let x = the length of ED and y = the length AJ. Then this tripleequation becomes
What's AD? So we can break our triple equation into these two equations:
and
So now you have two equations with two unknowns (x and y). It is easiest in this case to solve the first equation for y, solve the second equation for x, then substitute for y in the second equation to complete the solution and come up with an expression for x in terms of just the known values R and r. There is some longwinded but straightforward algebra which you should work out yourself. Hint: Don't multiply out squared expressions that you don't have to. My answer (which I've checked with r = 1 and R = 4), is Hope this helps,  


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