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Consider a uniform metal ring. Between points A and B a resistance of \(20\Omega\) is measured. What is the resistance between points A and C?

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so I set it up like I just drew above. The answer is \(20 \Omega\) but I can't figure out why, I keep getting \(15\Omega\). I know from A to B has resistance \(20\Omega\) so I put\[R_{AB}=\frac{2R(R+R)}{2R+(R+R)}=\frac{4R^2}{4R}=R=20\Omega\]So this is the value of R right? Then I do the same thing for between A & C and get\[R_{AC}=\frac{R(2R+R)}{R+(2R+R)}=\frac{3R^3}{4R}=\frac{3}{4}R=15\Omega\]

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Other answers:

does anyone see where I am going wrong?
answer is 20 ohm?
in 2nd expression...3/4 R...why u r putting R=20 ohm?
u have been given...resistance between points A and B is 20 ohm.. but u r using R(Ac) or R(CB)= 20 ohm....which is wrong.
does it help u?
Are the lengths given more precisely?
like A and B are halfway around the circle, and C is 1/4 the way from A?
you there?

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