Let A B C be an acute-angled triangle and let D be the mid-point of B C . If A B = A D , then tan B tan C equal

Step-by-step solution

In ∆ A B C , D be the mid-point of B C and A B = A D ⇒ Δ A B D is isosceles. Let A M be the perpendicular drawn from A to B C . ∴   A M is perpendicular bisector of B D B M = M D ln   Δ A B M ,   tan B = A M B M ln   Δ A M C ,   tan C = A M C M ∴   tan B tan C = C M B M = 3 B M B M = 3    ∵ C M = D M + C D