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MHT CET202525 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle A B C , with usual notations. 2 A a + B b + 2 C c = a b c + b c a Then A =

Options

  1. A4
  2. B6
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

Given the equation: 2 A a + B b + 2 C c = a b c + b c a Apply the cosine rule to express trigonometric terms: A = b^2 + c^2 - a^2 2 b c , B = a^2 + c^2 - b^2 2 a c , C = a^2 + b^2 - c^2 2 a b Substitute into the left-hand side: align* LHS &= 2 a b^2 + c^2 - a^2 2 b c + 1 b a^2 + c^2 - b^2 2 a c + 2 c a^2 + b^2 - c^2 2 a b &= b^2 + c^2 - a^2 a b c + a^2 + c^2 - b^2 2 a b c + a^2 + b^2 - c^2 a b c align* Combine terms over a common denominator of 2 a b c : 2(b^2 + c^2 - a^2) + (a^2 + c^2 - b^2) + 2(a^2 + b^2 - c^2) 2

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