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Math Help - Angles in a triangle

  1. #1
    Newbie Trikotnik's Avatar
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    Angles in a triangle

    It's a bit hard for me to translate math problems to english, but I think you'll be able to understand it:

    Points A, B and C are on a circle. The arc between A and B is 1/12 of the circle's perimeter, the arc between B and C is 1/6 of the perimeter. What are the angles of the triangle ABC?


    Oh yeah, is this even in the correct section of the forum?
    Last edited by Trikotnik; September 1st 2010 at 04:26 PM. Reason: Afterthought
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  2. #2
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    Quote Originally Posted by Trikotnik View Post
    It's a bit hard for me to translate math problems to english, but I think you'll be able to understand it:

    Points A, B and C are on a circle. The arc between A and B is 1/12 of the circle's perimeter, the arc between B and C is 1/6 of the perimeter. What are the angles of the triangle ABC?


    Oh yeah, is this even in the correct section of the forum?
    familiar with the angle measures of arcs?

    each angle is an inscribed angle in the circle ... there is a theorem that states that an inscribed angle is 1/2 the measure of its intercepted arc.

    angle A = 1/2 of arc BC

    angle B = 1/2 of major arc AC

    angle C = 1/2 of arc AB
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  3. #3
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    We know that the circumference of a circle is, C=2* \pi*r. Using the information given in the problem, this means that the length of the arc between A and B is (r* \pi)/6 and between B and C is (r* \pi)/3.

    Secondly, we know that s=r* \theta where s is the arc length, r is your radius, and \theta is the angle.

    Rearranging the above equation will allow you to solve for two of the angles. Simply subtracting them from the total degrees in a triangle will give you the third.
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  4. #4
    Newbie Trikotnik's Avatar
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    @cheme
    But how can I use any of the equations containing r if I don't have the lenght of the radius? Should I just make it up?


    Is it even possible to solve this without any additional information?



    Edit: @skeeter
    I just realised what a major arc is. Thanks. Problem Solved.

    α=30
    β=135
    γ=15
    Last edited by Trikotnik; September 1st 2010 at 05:41 PM.
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  5. #5
    Newbie Trikotnik's Avatar
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    Just wanted to say that I passed the test. Thanks a lot, skeeter, I'll definitely recommend this portal to friends.
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