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MHT CET202523 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In A B C , with usual notations, if B 2 = c+a 2 a , then a^2=

Options

  1. Ab^2-c^2
  2. Bb+c
  3. Cb^2+c^2
  4. Db-c

Correct answer

C. b^2+c^2

Step-by-step solution

In triangle ABC , the given relation is B 2 = c+a 2a . Squaring both sides yields ^2 B 2 = c+a 2a . Using the identity B = 2 ^2 B 2 - 1 , we substitute to obtain 2 ( c+a 2a ) = 1 + B , which simplifies to c+a a = 1 + B . Solving for B gives B = c+a a - 1 = c a . Applying the Law of Cosines at angle B : b^2 = a^2 + c^2 - 2ac B . Substituting B = c a produces b^2 = a^2 + c^2 - 2ac c a = a^2 + c^2 - 2c^2 = a^2 - c^2 . Rearranging gives a^2 = b^2 + c^2 , which corresponds to option C . The final answer is C .

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