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MHT CET202523 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC with usual notations. A 2 + B 2 + C 2 =

Options

  1. As^2 , where is the area of the triangle A B C .
  2. Bs , where is the area of the triangle A B C .
  3. Cs , where is the area of the triangle A B C .
  4. D, where is the area of the triangle A B C .

Correct answer

A. s^2 , where is the area of the triangle A B C .

Step-by-step solution

Using the half-angle cotangent formulas for triangle ABC , with semi-perimeter s = a+b+c 2 and area : A 2 = s(s-a) , B 2 = s(s-b) , C 2 = s(s-c) The sum becomes: A 2 + B 2 + C 2 = s(s-a) + s(s-b) + s(s-c) = s[(s-a) + (s-b) + (s-c)] Simplifying the numerator: s[(s-a) + (s-b) + (s-c)] = s[3s - (a+b+c)] = s[3s - 2s] = s^2 Thus: A 2 + B 2 + C 2 = s^2 This corresponds to option A .

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