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Question:

Given b+c/11 = c+a/12 = a+b/13 for a ΔABC with usual notation. If cosA/α = cosB/β = cosC/γ, then the ordered triad (α,β,γ) has a value:

(3,4,5)

(19,7,25)

(5,12,13)

(7,19,25)

Solution:

The correct option is C (7,19,25)
b+c=11λ, c+a=12λ, a+b=13λ
⇒a=7λ, b=5λ, c=6λ (using cosine formula)
cosA = 15, cosB = 19/35, cosC = 5/7
α:β:γ ⇒ 7:19:25