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> $r\_1$ and $r\_2$ are ex-radii about side a and b respectively. $\Delta$ is area of triangle. s is the semi-perimeter
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Since $r\_1=\frac{\Delta}{s-a}$
$$\Delta=s-a$$ and $$\Delta=2(s-b)$$

From this, it can be observed that 
$$b-a=\frac{\Delta}{2}$$ and $$c=\frac{3\Delta}{2}$$

How should I proceed ?