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Thread: Length of a curved triangle on a circle

  1. #1
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    Length of a curved triangle on a circle

    Hi there! New to the forum so, hi guys!

    Sorry if this is an easy one but my mind's gone blank on this. Trying to work out the length of the red line in the attached picture, given the radius of the circle, the length of the (quasi) adjacent side and the top angle.

    Thanks for any help or the equation for this!

    Cheers guys,

    PA
    Attached Thumbnails Attached Thumbnails Length of a curved triangle on a circle-curved-triangle.png  
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  2. #2
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    Re: Length of a curved triangle on a circle

    draw another radius to form a triangle and use the law of sines
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  3. #3
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    Re: Length of a curved triangle on a circle

    Gotcha, sorry I was having a real brain fart there, of course two triangles are possible given the variables.
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  4. #4
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    Re: Length of a curved triangle on a circle

    one triangle
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  5. #5
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    Re: Length of a curved triangle on a circle

    Quote Originally Posted by Idea View Post
    one triangle
    Length of a curved triangle on a circle-unt0.gif
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  6. #6
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    Re: Length of a curved triangle on a circle

    Quote Originally Posted by Plato View Post
    Click image for larger version. 

Name:	Unt0.gif 
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ID:	38591
    Yes two triangles possible depending on point A or D
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  7. #7
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    Re: Length of a curved triangle on a circle

    Quote Originally Posted by psychoangus View Post
    Yes two triangles possible depending on point A or D
    Only one triangle makes sense for finding the arc length you are looking for...
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  8. #8
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    Re: Length of a curved triangle on a circle

    Quote Originally Posted by SlipEternal View Post
    Only one triangle makes sense for finding the arc length you are looking for...
    Yes of course! I'm just saying, the maths could be done to give two possible outcomes.
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  9. #9
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    Re: Length of a curved triangle on a circle

    Quote Originally Posted by SlipEternal View Post
    Only one triangle makes sense for finding the arc length you are looking for...
    Quote Originally Posted by psychoangus View Post
    Yes of course! I'm just saying, the maths could be done to give two possible outcomes.
    If we look at this attachmentLength of a curved triangle on a circle-unt0.gif
    If $\overline{BA}$ were tangent to the circle then the question is trivial. But that is not given.

    We do know that $\frac{1}2{}(\hat{DE}-\hat{AF})=\frac{\pi}{3}$ The are $m(\hat{FDE})=\pi$
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  10. #10
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    Re: Length of a curved triangle on a circle

    Yep thanks for all your help guys.
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