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AP EAMCET20225 Jul 2022Morning ShiftMathematicsProperties of TrianglesActual

In any A B C, A a + B b + C c =

Options

  1. Aa^2+b^2+c^2
  2. Ba^2+b^2+c^2 2 a b c
  3. C2 a b c a^2+b^2+c^2
  4. Da+b+c

Correct answer

B. a^2+b^2+c^2 2 a b c

Step-by-step solution

Given, in a A B C , A a + B b + C c We know that, aligned & 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 aligned Since, b^2+c^2-a^2 2 a b c + a^2+c^2-b^2 2 a b c + a^2+b^2-c^2 2 a b = b^2+c^2-a^2+a^2+c^2-b^2+a^2+b^2-c^2 2 a b c = a^2+b^2+c^2 2 a b c

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