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Difference between length of arc and length of minor arc.

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ssy Rising GMAT Star
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Difference between length of arc and length of minor arc. Sat Oct 27, 2007 9:59 pm
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What is the difference between these two formulas? When do we use which?

Length of arc= (degree of arc/360)[(2)(pi)(radius)]

and

Length of minor arc = (2)(angle of arc)

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Mon Oct 31, 2011 3:55 am
ssy wrote:
What is the difference between these two formulas? When do we use which?

Length of arc= (degree of arc/360)[(2)(pi)(radius)]

and

Length of minor arc = (2)(angle of arc)
This is an old post, but it comes up when you search for GMAT + length of arc. I had the same question and the first response given above has two links, first of which doesn't work.
I did some research and my own analysis and am presenting my answer, hope this helps anybody else who stumbles upon this post:

Length of minor arc = (degree of arc/360)[(2)(pi)(radius)

Now, degree of arc = central angle inscribed by this arc.
Central angle, as the name suggests, is inscribed in the center; i.e. the vertex of the anle is the center of the circle. Central angle inscribed by an arc is twice the angle inscribed by the arc outside (in the circumference of the circle). This is what angle of arc in the first equation is.
i.e. Length of arc = 2 angle of arc *2(pi)(r)/360 = central angle * 2(pi)(r)/360.

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