Question

In a triangle $ABC$, if $\cot A,\cot B,\cot C$ are in A.P

then $a^2,b^2,c^2$ are in?

• A. H.P.
• B. A.P.
• C. G.P.
• D. None of the above

Answer 1

Answer: (B)

A.P.

if $cotA,cotB,cotC$ are in A.P.

then, $2cotB=cotA+cotC$ $\Rightarrow 2\frac{c^2+a^2-b^2}{4△}=\frac{b^2+c^2-a^2+a^2+b^2-c^2}{4△}\Rightarrow 2c^2+2a^2-2b^2=2b^2\Rightarrow c^2+a^2=2b^2$

Hence, $a^2,b^2,c^2$ are in A.P.

Therefore, Answer is $B$