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Given the expression to calculate the square of the radius of an incircle of a triangle is

$r^2 = {\frac{(s-a)(s-b)(s-c)}{s}}$

Given $a,b,r$ are known can the value of $c$ be found out without a quadratic equation ? Here $s$ stands for the semi perimeter which is $s={\frac{a+b+c}{2}}$

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  • $\begingroup$ The quadratic equation is useful, but never required. You can always complete the square instead. In this case, there's no c^2, so it's possible this isn't even a quadratic equation (s^2 does appear in the problem, but you're not solving for s). $\endgroup$ – barrycarter Jan 19 '17 at 16:57
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    $\begingroup$ @barrycarter Yes there is $c^2$ just by simplifying the above expression in order to get $c$ as the subject of the formula we land up with $c^2$. Could please show me how you are not ending up with any squares ? $\endgroup$ – ng.newbie Jan 19 '17 at 17:00
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    $\begingroup$ @barrycarter Please see what $s$ really stands for. $\endgroup$ – ng.newbie Jan 19 '17 at 17:01
  • $\begingroup$ My mistake, so I'll stick to my first comment: completing the square can always replace the quadratic equation. $\endgroup$ – barrycarter Jan 19 '17 at 17:03
  • $\begingroup$ @ng.newbie That equation is a cubic in $c\,$, not a quadratic. $\endgroup$ – dxiv Jan 19 '17 at 17:04

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