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AP EAMCET20227 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

Let A B C be an acute-angled triangle with area R . Then, a^2 b^2-4 R^2 + b^2 c^2-4 R^2 + c^2 a^2-4 R^2 =

Options

  1. Aa+b+c
  2. Ba^2+b^2+c^2
  3. Ca^2+b^2+c^2 2
  4. D2 (a^2+b^2+c^2 )

Correct answer

C. a^2+b^2+c^2 2

Step-by-step solution

aligned & a^2 b^2-4 R^2 = a^2 b^2-(a b c)^2 . & =a b C aligned Similarly, b^2 c^2-4 R^2 =b c A c^2 a^2-4 R^2 =c a B Given, expression aligned & =a b C+b c A+c a B & = a^2+b^2-c^2 2 + b^2+c^2-a^2 2 + c^2+a^2-b^2 2 & = a^2+b^2+c^2 2 aligned

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