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to see an image of what I'm talking about click this link: https://i.gyazo.com/909ccf0113fd26d21797f411a756ba1e.png In this image, arclength A is what we desire to be calculated. Point P is given and chord length C is given.

Given a point P and Chord length C, how do I calculate the arclength A in either side to create a chord of length C when a chord is created between the points both an arclength A away from point P are connected.

To do this I can take an iterative approach, trying arclengths until a chord of the desired length can be produced. However, I was wondering if a mathematical approach was possible.

In my specific problem, I define a point P along the circumference of an ellipse as the arclength distance from the point at theta=0. In other words, I evaluate the arclength from theta=0 to the theta characteristic of the point P to get the arclength parameter using the method described here: How to determine the arc length of ellipse?

This is fairly easily doable on a circle, but on an ellipse the arclength is not as easily as s=r*theta, but instead involves elliptic integrals, which I am not familiar with.

Thanks in advance for your help!

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Daniel Solnik
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http://www.ijsrp.org/research-paper-0813/ijsrp-p20103.pdf Solves it! The factor PI/(2root(2))[which I must write F (farooque) factor], which when multiplied to the chord length between any two points on curve gives the length of corresponding arc.)

Daniel Solnik
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