In triangle `A B C ,` if `cotA ,cotB ,cotC` are in `AdotPdot,` then `a^2,b^2,c^2` are in ____________ progression.

Options

A. HP
B. GP
C. AP
D. None of these

Answer

C

Explanation

Since, `cotA+cot C=2cotB`
`=(cosA)/(sinA)+(cosC)/(sinC)=(2cosB)/(sinB)`
`implies(b^(2)c^(2)_a^(2))/(2bc(ka))+(a^(2)+b^(2)-c^(2))/(2ab(kc))`
`=2(a^(2)+c^(2)-b^(2))/(2ac(kb))`
`impliesa^(2)+c^(2)=2b^(2)`
Hence, `a^(2),b^(2),c^(2)` are in AP.