A) AP
B) GP
C) HP
D) None of these
Correct Answer: A
Solution :
If\[{{r}_{1}},{{r}_{2}},{{r}_{3}}\]are in HP. \[\Rightarrow \] \[\frac{1}{{{r}_{1}}},\frac{1}{{{r}_{2}}},\frac{1}{{{r}_{3}}}\]are in AP. \[\Rightarrow \] \[\frac{s-a}{\Delta },\frac{s-b}{\Delta },\frac{s-c}{\Delta }\]are in AP. \[\left[ \because {{r}_{1}}=\frac{\Delta }{s-a},{{r}_{2}}=\frac{\Delta }{s-b},{{r}_{3}}=\frac{\Delta }{s-c} \right]\] \[\Rightarrow \] \[(s-a),(s-b),\text{(}s-c)\]are in AP. \[\Rightarrow \]a, b, c are in AP.
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