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Thread: Triangle in a cyrcle

  1. #1
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    Triangle in a cyrcle

    Does anyone know how to solve this? It has no information, just the answer is given, which is 72deg.
    Triangle in a cyrcle-screenshot_51.png
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  2. #2
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    Re: Triangle in a cyrcle

    Hey birkoof.

    You have an isosceles triangle, a hemi-circle and another circle [in the top].

    Try writing down as many variables as possible with your picture and show us the work you have done to write them as formulas so we can give you a hand.
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  3. #3
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    Re: Triangle in a cyrcle

    Well, inside the triangle I have 2alpha + beta = 180deg.
    Using the Angle in the Center Theorem I get a X that is two times bigger than my beta (beta = x/2)
    Implementing that in 2alpha + beta = 180deg i came with the result that alpha is equal to 90deg - x/4.
    That's all i can get from the information given.
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  4. #4
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    Re: Triangle in a cyrcle

    triangle with angles \beta ,\beta ,\alpha +\beta says \alpha +3\beta =180{}^{\circ}
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  5. #5
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    Re: Triangle in a cyrcle

    Quote Originally Posted by Idea View Post
    triangle with angles \beta ,\beta ,\alpha +\beta says \alpha +3\beta =180{}^{\circ}
    Thanks, this helped a lot. Now i just express  \beta from the first triangle, which is  180{}^{\circ} - 2 \alpha , put in the \alpha +3\beta =180{}^{\circ} and i get that  \alpha = 360{}^{\circ} /5 which is  72{}^{\circ} and the right answer. Thanks!
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