Question

In a triangle ABC if tan A/2 = $\frac { 5 } { 6 }$& tan $\frac { \mathrm { C } } { 2 }$ = $\frac { 2 } { 5 }$ , then –

• A. a, c, b are in A.P.
• B. a, b, c are in A.P.
• C. b, a, c are in A.P.
• D. a, b, c are in G.P.

Answer 1

Answer: (B)

a, b, c are in A.P.

Answer 2

tan tan $\frac { \mathrm { C } } { 2 }$ = $\frac { 2 } { 6 }$ = $\frac { 1 } { 3 }$

= $\frac { 1 } { 3 }$

⇒ $\frac { s - b } { s }$ = $\frac { 1 } { 3 }$

⇒ 3s – 3b = s ⇒ 2s = 3b ⇒ a + b + c = 3b

⇒ a + c = 2b