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Math Help - How to find a segment's length

  1. #1
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    How to find a segment's length


    Given the greatest angle and the circle radius I need to calculate the length of A segment.
    The circle is tangent to both lines.
    How can I do?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Let's call the centre of the smaller circle O, the point where the small circle touches the semi circle on the horizontal A, the other point which touches the semicircle B and the centre of the semicircle X.

    Angle AXB = 116 degrees.
    Angle OAX = angle OBX = 90 degrees.

    Find angle BOA.
    Once found, use the formula for the length of arc AB, that is s = r\theta

    Assuming that you are talking about this arc AB.

    A segment is an area. (Circular segment - Wikipedia, the free encyclopedia)
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  3. #3
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    Probably all those lines could confuse.
    I have 2 lines, S1 and S2, with a given angle beetween them (in this case is 116 degrees), then I have a circle tangent to both the lines with a given radius (in this case 20).
    I need to find a way to calculate the length of the segment AB.

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  4. #4
    MHF Contributor Unknown008's Avatar
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    Oh, that's what you mean. Ok, no problem.

    You now can find the angle AOB from your current diagram as I told you earlier. Well, let's call the point where the circle touches the other tangent X.

    You know that angle XAB = 116 degrees.
    That means angle XOB = 180 - 116 = 64 degrees.
    (or [360 - 90 - 90 - 116] since both tangents are 90 degrees)

    From there, the angle AOB becomes 64/2 = 32.

    From there, you use the trigonometrical ratio tan.

    tan 32 = Opp/Adj = AB/20

    Solve for AB.
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  5. #5
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    Thenks
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