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In a $\triangle A B C$, if $r_1>r_2>r_3$, then which of the following is true?
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The correct answer is:
$a>b>c$
$r_1>r_2>r_3$
$\begin{array}{ll}\Rightarrow & \frac{\Delta}{s-a}>\frac{\Delta}{s-b}>\frac{\Delta}{s-c} \\ \Rightarrow & (s-a) < (s-b) < (s-c) \\ \Rightarrow & -a < -b < -c \\ \Rightarrow & a>b>c\end{array}$
$\begin{array}{ll}\Rightarrow & \frac{\Delta}{s-a}>\frac{\Delta}{s-b}>\frac{\Delta}{s-c} \\ \Rightarrow & (s-a) < (s-b) < (s-c) \\ \Rightarrow & -a < -b < -c \\ \Rightarrow & a>b>c\end{array}$
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