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Math Help - Geometry Circle Problem

  1. #1
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    Geometry Circle Problem

    Geometry Circle Problem-mathstuff.pngPlease help me solve this.
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  2. #2
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    Re: Geometry Circle Problem

    Check your post...are you sure about the 120? Doesn't that look impossible to you?!
    Looks more as if the angle is 120 degrees, and you're to find arc's length...
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  3. #3
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    Re: Geometry Circle Problem

    Quote Originally Posted by Wilmer View Post
    Check your post...are you sure about the 120? Doesn't that look impossible to you?!
    Looks more as if the angle is 120 degrees, and you're to find arc's length...
    The measure of the arc is 120* as it says in the picture >.> and the measure of the arc is the same as the central angle, 120*.
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  4. #4
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    Re: Geometry Circle Problem

    I can't make out what you're saying...an arc has a LENGTH...perhaps someone else will...
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  5. #5
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    Re: Geometry Circle Problem

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

Name:	mathstuff.png 
Views:	15 
Size:	23.0 KB 
ID:	23506Please help me solve this.
    1. Have a look here: Inscribed angle - Wikipedia, the free encyclopedia

    2. As far as I understand your question you have to evaluate the length of the radius first. Use the indicated right triangle. Keep in mind that \sin(60^\circ) = \frac12 \sqrt{3}

    3. To determine the length of C use proportions:

    \frac C{2 \pi r}  = \frac{120^\circ}{360^\circ} = \frac13
    Attached Thumbnails Attached Thumbnails Geometry Circle Problem-centrwinkl_bogen.png  
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  6. #6
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    Re: Geometry Circle Problem

    Divide triangle into two right angled triangles
    Let r=radius. So sin60=3/r root3/2=3/r r=6/root3=6root3/3=2root3
    area sector 1/3pir^2 =1/3pi.12=4p


    Let height of triangle =h Then tan60=3/h h=3/tan60=root3
    Area of triangle=1/2.6.root3=3root3
    Segment=sector-triangl
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  7. #7
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    Re: Geometry Circle Problem

    That's not what's asked for, Biff.

    The problem, PROPERLY worded:
    chord AB = 6 cm
    angle AOB = 120 degrees
    calculate length of arc ACB

    ...to which Earboth shows the steps to solution.
    An arc SUPPORTS a central angle; is NOT equal to a number of degrees:
    it has its own length, which is part of the circle's circumference.
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  8. #8
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    Re: Geometry Circle Problem

    The problem asks for the angle AOB, sector area OACB,and segment areaACB.Biff in his last post defines sector area = 4pi and the sector triangle area 3rad3.Both correct.He didn't finish to find the segment area.
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  9. #9
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    Re: Geometry Circle Problem

    Area segment=area sector-area triangle=4pi-3root3
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