Question

If a,b,c are H.P., then $\frac{a}{b+c-a},\frac{b}{c+a-b},\frac{c}{a+b-c}$ are in

• A. $A.P$
• B. $H.P$
• C. G.P.
• D. none of these

Answer 1

The correct option is B $H.P$

Given,

$a,b,c$ in HP

$\frac{1}{a},\frac{1}{b},\frac{1}{c}$ in AP

$\frac{a+b+c}{a},\frac{a+b+c}{b},\frac{a+b+c}{c}$ in AP

$\frac{a+b+c}{a}-2,\frac{a+b+c}{b}-2,\frac{a+b+c}{c}-2$ in AP

$\frac{b+c-a}{a},\frac{a+c-b}{b},\frac{a+b-c}{c}$ in AP

$\frac{a}{b+c-a},\frac{b}{a+c-b},\frac{c}{a+b-c}$ in HP