My Math Forum Finding arc length

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 November 14th, 2016, 06:49 AM #1 Newbie   Joined: Nov 2016 From: Canada Posts: 1 Thanks: 0 Finding arc length I want to find the length of an arc with the following data: XYZ coordinates of start point XYZ coordinates of center point of the arc XYZ coordinates of end point arc direction Radius I can find the chord but there is 2 possible arcs with these values The arc is on a plane (XY,XZ,YZ) but I dont know which one Last edited by VincentP; November 14th, 2016 at 07:46 AM.
 November 14th, 2016, 12:21 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,369 Thanks: 1273 well as you've said there are two arcs that meet those conditions. fortunately if you know the arc length of one, $\ell_1$, the arc length of the other is just $\ell_2 = 2\pi r - \ell_1$
 November 14th, 2016, 01:44 PM #3 Global Moderator   Joined: May 2007 Posts: 6,704 Thanks: 669 If you know the coordinates of the center point of the arc, this will tell you which of the 2 possible arcs defined by the chord. This can be done by examining the chord from the end point to the midpoint of the arc. Compare it to $\displaystyle \frac{r\sqrt{2}}{2}$. Less is the shorter angle, more is the longer angle. Last edited by mathman; November 14th, 2016 at 01:46 PM.

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