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MHT CET202618 April 2026Evening ShiftMathematicsProperties of TrianglesActual

In ABC , with usual notations, if denotes the area of triangle ABC then the value of 2s(b+c-a) ( A 2 ) is equal to

Options

  1. A2
  2. B3
  3. C4

Correct answer

3

Step-by-step solution

We know that the semi-perimeter of a triangle is given by s = a+b+c 2 , which implies 2s = a+b+c . The term b+c-a can be rewritten as: b+c-a = (a+b+c) - 2a = 2s - 2a = 2(s-a) Substituting this into the given expression, we get: 2s(b+c-a) ( A 2 ) = 2s(2(s-a)) ( A 2 ) = 4s(s-a) ( A 2 ) Using the half-angle formula for tangents in a triangle: ( A 2 ) = (s-b)(s-c) s(s-a) Multiplying the numerator and the denominator inside the square root by s(s-a) gives: ( A 2 ) = s(s-a)(s-b)(s-c) s(s-a) By Heron's formula, the area o

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