Question

If the sides a, b, c of a triangle ABC are in A.P. then $\frac{b}{c}$ belongs to

• A. $\left( 0,\frac{2}{3} \right)$
• B. (1, 2)
• C. $\left( \frac{2}{3},2 \right)$
• D. $\left( \frac{2}{3},\frac{7}{3} \right)$

Answer 1

Answer: (C)

$\left( \frac{2}{3},2 \right)$

Answer 2

a = 2b – c

a + b > c Ž 2b – c + b > c Ž $\frac{b}{c} > \frac{2}{3}$

Also b + c > a Ž b + c > 2b – c Ž $\frac{b}{c}$ < 2

Again c + a > b Ž 2b > b

$\frac{b}{c}$ Ī $\left( \frac{2}{3},2 \right)$