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Thread: Distance across a circle

  1. #1
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    Distance across a circle

    Hi there, I'm writing a computer program and I'm having a problem with the geometry. I would be very grateful for any help.
    My problem is that i have one fixed point on a circles perimeter and one point which is moving around the perimeter. Do you know how i can calculate the distance between the points at any time? I should add that i know the radius and the angle at which the moving point is in relation to the fixed. Does such a formula exist?
    Anyway, thanks for your time and any help would be amazing!
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  2. #2
    A Plied Mathematician
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    If $\displaystyle d$ is the distance between two points on a circle of radius $\displaystyle a$, and the angle subtended by the two radii to the two points is given by $\displaystyle \theta,$ then we can use the Law of Cosines to compute the distance:

    $\displaystyle d^{2}=a^{2}+a^{2}-2(a)(a)\cos(\theta).$

    Can you simplify?
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    If $\displaystyle d$ is the distance between two points on a circle of radius $\displaystyle a$, and the angle subtended by the two radii to the two points is given by $\displaystyle \theta,$ then we can use the Law of Cosines to compute the distance:

    $\displaystyle d^{2}=a^{2}+a^{2}-2(a)(a)\cos(\theta).$

    Can you simplify?
    Thank you very much this is just what i'm looking for. I couldn't find the right expression anywhere. Thanks for your time and help!!
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  4. #4
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    You're welcome. Have a good one!
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