SOLUTION: How do you find the radius of a circle inscribed into a scalene triangle

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Question 1105669: How do you find the radius of a circle inscribed into a scalene triangle
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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The radius of a  circle inscribed in a scalene triangle is equal to the area of the triangle divided by semi-perimeter:


r = A%2Fs,     (1)


where A is the area and "s" is the semi-perimeter.


Or, equivalently, A = r*s.


For the proof, see the lesson
    - Proof of the formula for the area of a triangle via the radius of the inscribed circle 
in this site.


So, if you know the side lengths of your scalene triangle, you can calculate its area using the Heron's formula, and then use the formula (1).


On Heron's formula, see the lessons
    - Proof of the Heron's formula for the area of a triangle 
    - One more proof of the Heron's formula for the area of a triangle 
in this site.