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I have two circles.

 

( x - (1-b) )²   +   y² = b²

 

( x - cos(120°) * (1-b) )²   +   ( y - sin(120°) * (1-b) )² = b²

 

My question is: for what value of "b" causes these two circles meet at exactly one point?

 

I tried this with some geometry and I THINK the answer is b = 2sqrt(3) - 3 or ≈ 0.46410165...

 

I think this can be solved with calculus but I don't know how to begin. Any help would be appreciated.

 

(note: it may take me a while to reply back to this thread, but I will eventually reply, I promise!)

 

(another note: there is a third circle in this problem, just replace 120° with 240°, but the answer I need will be the same as the answer from the problem above, so don't worry about it)

 
 Jan 2, 2017
edited by LambLamb  Jan 2, 2017
edited by LambLamb  Jan 2, 2017

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