# Define Circle Knowing Two Points and ARC LENGTH Only.

Ryank
I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I realize there would be two distinct solutions depending on positive of negative curvature. Any help would be amazing, thanks!

Mentor
I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I realize there would be two distinct solutions depending on positive of negative curvature. Any help would be amazing, thanks!

What is the context of the question? Could you post a sketch? Thanks.

Ryank
There doesn't really need to be a context. You know the length of a chord on the circle and the length of the arc segment between them. I did some digging and did finally manage to find two solutions. One uses Newton's approximation method and the other uses and taylor expansion:

http://www.mathforum.com/dr.math/faq/faq.circle.segment.html#1 [Broken]

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Homework Helper
Looks like case 1 from Dr. Math that requires Newton's Method is the most straightforward.

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Studiot
Perhaps this sketch will help, it's basic trigonometry.

Since you have fixed two points on the circumference you not only know the arc length you also know the chord length.

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