Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Find the radius of the circumscribed circle

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    Malaysia
    Posts
    24

    Find the radius of the circumscribed circle

    Given that in a triangle ABC, AB = 2cm, AC = 3cm, \angle A =60^\circ Find the radius of the circumscibed circle of ABC.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,653
    Thanks
    1478

    Re: Find the radius of the circumscribed circle

    Quote Originally Posted by shiny718 View Post
    Given that in a triangle ABC, AB = 2cm, AC = 3cm, \angle A =60^\circ Find the radius of the circumscibed circle of ABC.
    We know that the three vertices of the triangle lie on a circle. If we say that point A is the origin (0, 0), then we could say that since the length AC is 3 cm, the co-ordinate of C is (3, 0).

    We know that point B lies 2cm from point A making an angle of \displaystyle \begin{align*} 60^{\circ} \end{align*}.

    The vertical position of point B can be found by

    \displaystyle \begin{align*} \sin{60^{\circ}} &= \frac{y}{2} \\ \frac{\sqrt{3}}{2} &= \frac{y}{2} \\ y &= \sqrt{3} \end{align*}

    and the horizontal position of point B can be found by

    \displaystyle \begin{align*} \cos{60^{\circ}} &= \frac{x}{2} \\ \frac{1}{2} &= \frac{x}{2} \\ x &= 1 \end{align*}

    So point B is at \displaystyle \begin{align*} \left(1, \sqrt{3}\right) \end{align*}.


    Now that you have three points that lie on your circle, you can substitute them into the general equation for a circle \displaystyle \begin{align*} (x - h)^2 + (y - k)^2 = r^2 \end{align*} and solve them simultaneously for \displaystyle \begin{align*} h, k, r \end{align*} (you are trying to find r).
    Thanks from shiny718
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: Find the radius of the circumscribed circle

    You can find BC either by using law of cosines or by constructing an altitude from point B and using 30-60-90 triangles. Either way, you should get BC = \sqrt{7}.

    There is a formula for the area of a triangle, [ABC] = \frac{AB*BC*CA}{4R}, where R is the circumradius. We know AB, BC, CA, and just need to find the area. This is easy, since

    [ABC] = \frac{1}{2}AB*BC*\sin{A} = \frac{1}{2}(2)(3)(\frac{\sqrt{3}}{2}) = \frac{3 \sqrt{3}}{2}


    Hence, \frac{3 \sqrt{3}}{2} = \frac{2*3*\sqrt{7}}{4R}

    12R \sqrt{3} = 12 \sqrt{7}

    R = \frac{\sqrt{7}}{\sqrt{3}} = \frac{\sqrt{21}}{3}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 29th 2011, 10:26 PM
  2. Find radius of circle
    Posted in the Geometry Forum
    Replies: 8
    Last Post: August 28th 2010, 06:04 PM
  3. Replies: 2
    Last Post: February 6th 2010, 08:31 AM
  4. Find radius of circle..
    Posted in the Geometry Forum
    Replies: 5
    Last Post: March 22nd 2007, 04:17 AM
  5. find the radius of this circle
    Posted in the Geometry Forum
    Replies: 5
    Last Post: November 15th 2005, 08:05 AM

Search Tags


/mathhelpforum @mathhelpforum