1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook