Calculating Circular Arc Length: Radius, Angle, and Unknown Center

[jrm2002]

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?

 

[Defennder]

Do you want to calculate the arc length of the major or minor arc?

 

[jrm2002]

That is the point--I have three points start,intermediate and end--if the centre of the circle is within the sector bounded by the three points I need the major arc length else if the canter of the circle is not within the sector bounded within the 3 points i need minor arc

 

[Defennder]

I don't get what you're trying to say here. You said you're given angle subtended by the starting and ending point. Is that angle always <180 degrees? If not, then that means it's clear whether they want the major or minor arc. If it always is smaller than 180, then you have got to check the question to see which arc length they require. They shouldn't be that ambiguous about this.