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MHT CET202520 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle ABC with usual notations, if a , b , c are in arithmetic progression, then, A 2 C 2 =

Options

  1. A3
  2. B1 13
  3. C-3
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

Given triangle ABC with sides a , b , c in arithmetic progression, we have 2b = a + c . The semi-perimeter is s = a + b + c 2 . Substituting a + c = 2b yields s = 3b 2 . The product of tangents of half-angles satisfies: A 2 C 2 = s - b s Substituting s = 3b 2 gives: A 2 C 2 = 3b 2 - b 3b 2 = b/2 3b/2 = 1 3 Final answer: 1 3

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