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Question

Question: In a triangle ABC, and , then...

In a triangle ABC, and , then

A

are in A.P.

B

are in A.P.

C

are in A.P.

D

Both (1) and (3)

Answer

Both (1) and (3)

Explanation

Solution

tan⁡A2⋅tan⁡C2=(s−b)s\tan \frac { A } { 2 } \cdot \tan \frac { C } { 2 } = \frac { ( s - b ) } { s } ⇒ 56⋅25=s−bs\frac { 5 } { 6 } \cdot \frac { 2 } { 5 } = \frac { s - b } { s }

⇒ 2s=3b⇒a+b+c=3b⇒a+c=2b2 s = 3 b \Rightarrow a + b + c = 3 b \Rightarrow a + c = 2 b .