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Question Number 185128 by Shrinava last updated on 17/Jan/23

	Answered by Frix last updated on 17/Jan/23

	$Formulas for incircle and 3 excircles :$ $r = \frac{2 A}{a + b + c}$ $r_{a} = \frac{2 A}{b + c - a}$ $r_{b} = \frac{2 A}{a + c - b}$ $r_{c} = \frac{2 A}{a + b - c}$ $A^{2} = {r r}_{a} r_{b} r_{c}$ $\Rightarrow$ $- a + b + c = \frac{2 A}{1} = 2 A$ $a - b + c = \frac{2 A}{4} = \frac{A}{2}$ $a + b - c = \frac{2 A}{12} = \frac{A}{6}$ $\Rightarrow$ $a = \frac{A}{3} \land b = \frac{13 A}{12} \land c = \frac{5 A}{4}$ $\Rightarrow r = \frac{3}{4}$ $\Rightarrow A = 6$
	Commented by Shrinava last updated on 17/Jan/23

	$dear ser answer : 6 or 36 ?$
	Commented by Shrinava last updated on 17/Jan/23

	$but answer : 6$
	Commented by Frix last updated on 17/Jan/23

	$I corrected it$
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