Question
In a triangle with sides $$a, b, c,$$ $${r_1} > {r_2} > {r_3}$$ (which are the ex-radii) then
A.
$$a > b > c$$
B.
$$a < b < c$$
C.
$$a > b$$ and $$b < c$$
D.
$$a < b$$ and $$b > c$$
Answer :
$$a > b > c$$
Solution :
$$\eqalign{
& {r_1} > {r_2} > {r_3} \cr
& \Rightarrow \,\,\frac{\Delta }{{s - a}} > \frac{\Delta }{{s - b}} > \frac{\Delta }{{s - c}}; \cr
& \Rightarrow \,\,s - a < s - b < s - c \cr
& \Rightarrow \,\, - a < - b < - c \cr
& \Rightarrow \,\,a > b > c \cr} $$