If median of the `Delta`ABC through A is perpendicular to BC, then which one of the following is correct ?

Options

A. tan A + tan B = 0
B. tan B - tan C = 0
C. tan C + 2 tan A = 0
D. tan B + tan C = 0

Answer

B

Explanation

In the given `Delta`ABC let BC = a
`therefore BD = CD =(a)/(2)`
In `Delta`ADB, `tanB=(AD)/(BD)=(AD)/(a//2)`
`rArr tan B = (2AD)/(a)" "...(1)`
In `Delta`ADC, `tan C = (AD)/(CD)=(AD)/(a//2)`
`tan C = (2AD)/(a)" "...(2)`
From eqs. (1) and (2), we get tan B = tan C
`rArr tan B - tan C = 0`