Question

The exradii of a triangle, $r_1,r_2,r_3$ are in 1A armonic progression, then the sides a, b and c are in

• A. HP
• B. AP
• C. GP
• D. None of these

Answer 1

Answer: (B)

It is given that $r_1,r_2$ and $r_3$ are in HP. $\Rightarrow$ $\frac{2}{r_2}=\frac{1}{r_1}+\frac{1}{r_3}$ $\Rightarrow$ $\frac{2(s-b)}{\Delta }=\frac{s-a}{\Delta }+\frac{s-c}{\Delta }$ $\Rightarrow$ $2a-2b=2s-a-c$ $\Rightarrow$ $2b=a+c$ Hence, a, b and c are in AP