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MHT CET202520 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , with usual notations if 2 ~A a + B b + 2 C c = a bc + b c a then A =

Options

  1. A2
  2. B4
  3. C3
  4. D6

Correct answer

A. 2

Step-by-step solution

Substituting the cosine rule expressions into the given equation: A = b^2+c^2-a^2 2bc , B = a^2+c^2-b^2 2ac , C = a^2+b^2-c^2 2ab 2 a b^2+c^2-a^2 2bc + 1 b a^2+c^2-b^2 2ac + 2 c a^2+b^2-c^2 2ab = a^2+3b^2+c^2 2abc The right side simplifies to a^2+b^2 abc . Equating both sides: a^2+3b^2+c^2 2abc = a^2+b^2 abc Multiplying through by 2abc and simplifying yields: b^2 + c^2 = a^2 This is the Pythagorean relation, indicating that angle A opposite side a is 90^ or 2 radians. The correct option is A .

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