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MHT CET202616 April 2026Morning ShiftMathematicsProperties of TrianglesActual

With usual notations in ABC, if b ^2 C 2 + c ^2 B 2 = 3a 2 then

Options

  1. Aa, b, c are in A.P.
  2. Ba, c, b are in A.P.
  3. Cb, a, c are in A.P.
  4. Da, b, c are in G.P

Correct answer

C. b, a, c are in A.P.

Step-by-step solution

Given b ^2 C 2 + c ^2 B 2 = 3a 2 Using the half-angle formula ^2 2 = 1 + 2 , the equation becomes: b ( 1 + C 2 ) + c ( 1 + B 2 ) = 3a 2 Multiplying by 2 on both sides: b + b C + c + c B = 3a Rearranging the terms: b + c + (b C + c B) = 3a Using the projection formula a = b C + c B : b + c + a = 3a b + c = 2a This condition implies that b, a, c are in A.P. Answer: b, a, c are in A.P.

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