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Circumcircle of a triangle.

  1. Feb 8, 2005 #1
    For a triangle, 3 sides are given.
    What's the radius of its circumcircle?
    Are we able to get it without using cosine law or sine law or heron formula?
  2. jcsd
  3. Feb 8, 2005 #2
    What is a circumcircle?
  4. Feb 8, 2005 #3
    An outern circle .
  5. Feb 8, 2005 #4
    I'm really sorry, but I have no idea what you are talking about.
  6. Feb 8, 2005 #5
    A circle surrounds a triangle, the three vertexs of the triangle touches the circumference
  7. Feb 8, 2005 #6
    Oh, I apologize. The only way which I know of to get that is with the law of cosines.
  8. Feb 8, 2005 #7
    My teachers haven't taught us the cosine law, but this question is in the part of properties of circle. Moreover, he hasn't taught heron formula.
  9. Feb 9, 2005 #8


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  10. Feb 10, 2005 #9


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    First, use the law of cosine:
    [tex]a^{2} = b^{2} + c^{2} - 2bc\cos{A}[/tex]
    [tex]b^{2} = a^{2} + c^{2} - 2ac\cos{B}[/tex]
    [tex]c^{2} = a^{2} + b^{2} - 2ab\cos{C}[/tex]
    to find out cos of one of the angle in the triangle, then use [itex]sin^{2}\theta + cos^{2}\theta = 1[/itex] (In a triangle, [itex]sin\theta[/itex] is always positive) to find its sine and then use the law of sine to find out the radius of the circumcircle.
    The law of sine is:
    [tex]\frac{a}{\sin{A}} = \frac{b}{\sin{B}} = \frac{c}{\sin{C}} = 2 \times R[/tex]
    Where R is the radius of the circumcircle.
    Hope you get it.
    Viet Dao,
  11. Feb 11, 2005 #10
    No need sin law.
    I know many methods, but currently I want the most simpliest one.
    Anyway, thank you. :P
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