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Area of a circle within a circumscribed triangle

  1. Jan 31, 2012 #1
    If you have a triangle circumscribed around a circle, how do you find the area of that circle? Say that the triangle is an equilateral triangle with side length of 8 cm.

    I found the area of the triangle using Heron's formula: 16√3 cm^2. Apparently the answer is 16π/3 cm^2. I'm just confused as to how this answer was found. Any help would be appreciated. :smile:
     
  2. jcsd
  3. Jan 31, 2012 #2

    LCKurtz

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    Of course the circle will have a ##\pi## in its area formula. For the equilateral triangle draw a line from a vertex to the center of the circle and from the center perpendicular to an adjacent side. That will give you a 30-60-90 triangle with one leg = 4. From that you can get the radius of the circle.
     
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