In a $\triangle A B C$, if $r_1>r_2>r_3$, then which of the following is true?

In a $\triangle A B C$, if $r_1>r_2>r_3$, then which of the following is true?
  1. $a>b>c$
  2. $a>b, b < c$
  3. $a < b < c$
  4. $a < b, b>c$

Solution

$r_1>r_2>r_3$ $\begin{array}{ll}\Rightarrow & \frac{\Delta}{s-a}>\frac{\Delta}{s-b}>\frac{\Delta}{s-c} \\ \Rightarrow & (s-a) < (s-b) < (s-c) \\ \Rightarrow & -a < -b < -c \\ \Rightarrow & a>b>c\end{array}$

Asked in: AP EAMCET 2022 (08 Jul Shift 2)

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