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Define Circle Knowing Two Points and ARC LENGTH Only.

  1. Mar 18, 2010 #1
    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!
     
  2. jcsd
  3. Mar 18, 2010 #2

    berkeman

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    Staff: Mentor

    What is the context of the question? Could you post a sketch? Thanks.
     
  4. Mar 18, 2010 #3
    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://norman.rasmussen.co.za/24/radius-from-arc-and-chord-length/
    http://www.mathforum.com/dr.math/faq/faq.circle.segment.html#1 [Broken]
     
    Last edited by a moderator: May 4, 2017
  5. Mar 18, 2010 #4

    hotvette

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    Homework Helper

    Looks like case 1 from Dr. Math that requires Newton's Method is the most straightforward.
     
    Last edited: Mar 18, 2010
  6. Mar 18, 2010 #5
    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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