Question

Let f, g, h be the lengths of the perpendiculars from the circum centre of the ∆ABC on the sides a, b and c respectively.

If a/f + b/g + c/h = λ(abc/fgh) then the value of λ is

(A)1/4

(B)1/2

(C)1

(D)2

Answer 1

Correct option (A)1/4

Explanation:

OB = R

∠AOC = 2A, ∠BOD = A

f = OD = RcosA

L.H.S = a/f + b/g + c/h = a/RcosA + b/RcosB + c/RcosC

PutR = a/2sinA =  2(tanA + tanB + tanC) = 2tanA tanB tanC

R.H.S. = λ(abc/(R³cosAcosBcosB))

Put R = a/2sinA =  8λ tanA tanB tanC

⇒ λ = 1/4