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The median AD of a DeltaABC is perpendic...

The median `AD` of a `DeltaABC` is perpendicular to AB, than `tanA + 2tanB= `

A

tan A + tan B = 0

B

2 tan A + tan B = 0

C

tan A + 2tan B = 0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have BD = DC and `angle DAB = 90^(@)`. Draw CN perpendicular to BA produced, then in `Delta BCN`, we have `DA=(1)/(2)CN` and AB = AN

Let `angle CAN = alpha`
`because tan A = tan (pi - alpha)`
`= - tan alpha`
`=-(CN)/(NA)`
`=-2(AD)/(AB) (because Delta BAD ~ Delta BNC` and `AC = 2BD)`
`=-2 tan B`
`rArr tan A + 2 tan B = 0`
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