Question

If the sides a, b, c of a triangle ABC form successive terms of G.P. with common ratio r (> 1) then which of the following is correct -

• A. A >p/3
• B. B ³p/3
• C. C <p/3
• D. A < B <p/3

Answer 1

Answer: (D)

A < B <p/3

Answer 2

Let the sides of a triangle be a, ar, ar²

Q ar² is greater side (r > 1)

\ a + ar > ar²

cos C = = < $\frac { 1 } { 2 }$ Ž C > $\frac { \pi } { 3 }$

cos B = =

= $\frac { 1 } { 2 }$ $\left[ \mathrm { r } ^ { 2 } + \frac { 1 } { \mathrm { r } ^ { 2 } } - 1 \right]$

= $\frac { 1 } { 2 }$ $\left[ \left( \mathrm { r } - \frac { 1 } { 2 } \right) ^ { 2 } + 1 \right]$ >1/2 Ž B < p/3.

Also, a ar, ar² Ž A < B < C Ž A < B < $\frac { \pi } { 3 }$ < C.