Question

With usual notation, if in a triangle ABC (b + c)/11 = (c + a)/12 = (a + b)/13, then prove that cosA/7 = cosB/19 = cosC/25.

Answer 1

Let (b + c)/11 = (c + a)/12 = (a + b)/13 = λ

⇒ (b+ c ) = 11λ, c + a = 12λ, a + b = 13λ ... (i)

⇒ 2(a+ b + c) = 36λ

⇒ a + b +c = 18λ ... (ii)

On solving the Eqs. (i) and (ii), we get

a = 7λ , b = 6λ and c = 5λ