AIEEE 2002 (Offline)Question 1
In a triangle with sides $a,b,c$, if $r_1>r_2>r_3$ (which are the ex-radii) then :
Trigonometric Ratio & Identities
Solution
Concept. Each ex-radius is $\Delta$ divided by $s$ minus the matching side. Formulas used. (1) $r_1=\dfrac{\Delta}{s-a}$, $r_2=\dfrac{\Delta}{s-b}$, $r_3=\dfrac{\Delta}{s-c}$Step 1 - Compare. By (1), $r_1>r_2>r_3\iff s-a<s-b<s-c$. Step 2 - Conclude. That means $a>b>c$. Answer: (A)