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MHT CET202615 April 2026Morning ShiftMathematicsProperties of TrianglesActual

In ABC with usual notations, if 1 + ( A 2 ) ( B 2 ) = k s (where s is the semi-perimeter), then the value of k is...

Options

  1. A2
  2. Ba + b - c
  3. Ca + b
  4. Ds - c

Correct answer

C. a + b

Step-by-step solution

Using the half-angle formulas for a triangle: ( A 2 ) = (s-b)(s-c) s(s-a) ( B 2 ) = (s-a)(s-c) s(s-b) Multiplying these two expressions: ( A 2 ) ( B 2 ) = (s-b)(s-c) s(s-a) (s-a)(s-c) s(s-b) = s-c s Substituting this into the given equation: 1 + ( A 2 ) ( B 2 ) = 1 + s-c s = 2s - c s Since 2s = a + b + c , we have 2s - c = a + b . Therefore, 1 + ( A 2 ) ( B 2 ) = a + b s Comparing this with k s , we get k = a + b . Answer: a + b

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