- #1

Mentallic

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[tex]r^2-a^2=\sqrt{(r^2-a^2)(R^2-(b-d)^2)}[/tex]

[tex]\sqrt{(r^2-a^2)(R^2-(d-b)^2)}=R^2-d^2+bd-ab+ad[/tex]

Now wait, before you run off thinking "screw that - too many letters, too much hassle" I don't actually want you to solve this for me, but I have a question about it.

Firstly,

**r**,

**R**and

**d**are constants and I'm looking to solve for

**a**and

**b**so what I essentially want is:

[tex]a=f(r,R,d)[/tex] and [tex]b=f(r,R,d)[/tex] (I'm not even sure if I have expressed what I want properly, I just took a best guess at this. It translates into "a as a function in terms of r, R and d").

What I thought I'd try is, instead of expanding one equation and solving a quadratic in terms of one of the variables a or b, I'll eliminate the [tex]\sqrt{(r^2-a^2)(R^2-(d-b)^2)}[/tex] so what I end up having is:

[tex]R^2-d^2+bd-ab+ad=r^2-a^2[/tex]

but then this doesn't look like it's helping me solve for either variable. Is the only way I can solve for a and b by going through the long painful process of using the quadratic formula? Any other suggestions on a simpler approach I could take?