If the median of ΔABC through A is perpendicular to AB then
A
tanA+tanB=0
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B
2tanA+tanB=0
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C
tanA+2tanB=0
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D
None of these
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Solution
The correct option is C
tanA+2tanB=0
We have BD=DC and ∠DAB=900 Draw CN perpendicular to BA produced, then in ΔBCN, we have DA=12CN and AB=AN Let ∠CAN=α∵tanA=tan(π−α)=−tanα=−CNNA=−2ADAB=−2tanB⇒tanA+2tanB=0