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MHT CET202618 April 2026Morning ShiftMathematicsProperties of TrianglesActual

In triangle ABC, with usual notations, if (a+b+c)(a+b-c) = ab , then the measure of angle C is...

Options

  1. A2
  2. B2 3
  3. C5 6
  4. D3 4

Correct answer

B. 2 3

Step-by-step solution

Given (a+b+c)(a+b-c) = ab ((a+b)+c)((a+b)-c) = ab (a+b)^2 - c^2 = ab a^2 + b^2 + 2ab - c^2 = ab a^2 + b^2 - c^2 = -ab Using the cosine rule for C : C = a^2 + b^2 - c^2 2ab Substituting the value of a^2 + b^2 - c^2 : C = -ab 2ab = - 1 2 Since 0 Answer: 2 3

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