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MHT CET202520 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , with usual notations, 3 ~b = a + c , then A 2 c 2 =

Options

  1. A1
  2. B2
  3. C1 2
  4. D4

Correct answer

B. 2

Step-by-step solution

Using the semi-perimeter s = a+b+c 2 , the half-angle cotangent formulas yield: A 2 C 2 = s(s-a) (s-b)(s-c) s(s-c) (s-a)(s-b) = s s-b Given 3b = a + c , the semi-perimeter becomes s = (a+c)+b 2 = 3b+b 2 = 2b . Substituting into the product gives 2b 2b-b = 2 . Final Answer: B

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