Question

If the median of a triangle ABC through A is perpendicular to AB then tanA/tanB  has the value equal to

(A) 1/2

(B) 2

(C) - 2

(D) - 1/2

Answer 1

Correct option  (C) −2

Explanation:

BD = 1/2BC

Pythagoras theorem in ∆BAD 

c² + (AD)² = (BD)²

c² + 1/4(2b² + 2c² - a²) = a²/4

⇒ a² = b² + 3c²

tanA/tanB = sinA/sinB x cosB/cosA

= a/b((a² + c² - b²)/2ac) (2bc/(b² + c² - a²)) 

= (a² + c² - b²)/(b² + c² - a²) = - 2