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Question

In ABC, if cot A, cot B, cot C be in A. P. then a2,b2,c2 are in


A

H.P.

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B

G.P.

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C

A.P.

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D

None of these

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Solution

The correct option is C

A.P.


cot A, cot B and cot C are in A.P.
cot A + cot C = 2 cot B cos Asin A+cos Csin C=2 cos Bsin B
b2+c2a22bc(ka)+a2+b2c22ab(kc)=2a2+c2b22ac(kb)
a2+c2=2b2. Hence a2,b2,c2 are in A. P.


It might help to remember this result as a general relation.


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