How to prove the inequality arc length (AB) <= arc length (AC) + arc length(BC) for any point A,B,C on a cylinder?

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I need to use the formula of arc length(r) = ((a-b)^2+(x-y)^2)^1/2 for point A =(a, x) and B=(b,y), but I don't know how to expand the inequality and prove it.