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Circle Inscribed in a Triangle

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Calculates the radius and area of the incircle based on the three sides of a triangle.
Side length a
Side length b
Side length c
Radius of the Inscribed Circle r 
Diameter φ of the inscribed circle 
Area of the incircle Sc 
Area of a Triangle St 
Area ratio Sc/St 
\(\normalsize Incircle\ of\ a\ triangle\\ (1)\ incircle\ radius:\hspace{5px} r={\large\frac{\sqrt{s(s-a)(s-b)(s-c)}}{s}}\\ (2)\ incircle\ area:\ Sc=\pi r^2\\ (3)\ triangle\ area:\ St=\sqrt{s(s-a)(s-b)(s-c)}\\ \hspace{230px} s={\large\frac{a+b+c}{2}}\\\)

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