Question

If the median of $\Delta ABC$ through $A$ is perpendicular to $AB$ then

• A. $tanA+tanB=0$
• B. $2tanA+tanB=0$
• C. $tanA+2tanB=0$
• D. None of these

Answer 1

The correct option is C

$tanA+2tanB=0$

We have $BD=DC$ and $\angle DAB={90}^0$ Draw $CN$ perpendicular to $BA$ produced, then in $\Delta BCN,$ we have $DA=\frac{1}{2}CN$ and $AB=AN$

Let $\angle CAN=\alpha \because tanA=tan(\pi -\alpha )=-tan\alpha =-\frac{CN}{NA}=-2\frac{AD}{AB}=-2tanB\Rightarrow tanA+2tanB=0$