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Manipal MET2012MathematicsProperties of Triangles

If k be the perimeter of the A B C , then b ^2 C 2 +c ^2 B 2 is equal to

Options

  1. Ak
  2. B2 k
  3. Ck 2
  4. DNone of these

Correct answer

C. k 2

Step-by-step solution

aligned & b ^2 C 2 +c ^2 B 2 & = b 2 (1+ C)+ c 2 (1+ B) & = b 2 + c 2 + 1 2 (b C+c B) & = b 2 + c 2 + a 2 ( a=b C+c B) & = a+b+c 2 = k 2 aligned

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