(adsbygoogle = window.adsbygoogle || []).push({}); Circular arc--badly stuck

I have a circular arc defined by 3 points [start point, intermediate point an end point].

I know the radius of the circular arc too.

I know the angle subtended by the start and end point at the centre.

I do not know the center of the circle

Now,

I want to calculate the length of the arc using s = r * theta

"r" being the radius and "theta" the angle subtended by the start and end point at the centre.[theta being the smaller included angle]

Now, i get a length "L"

But in some problems my answer is correct value "L" but in some cases the answer i need is 2*pi - L [that corresponding to bigger included angle] but i get "L".This i checked graphically--

Howm to get the correct validation algebraically?

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# Circular arc-badly stuck

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