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MHT CET202521 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In A B C , with usual notations, a ~B = b A , a C c A then A ( ABC ) _____ sq. units.

Options

  1. Ac 2 4 a^2-b^2
  2. Bc 4 4 a^2-c^2
  3. Cb 2 4 b^2-c^2
  4. Db 4 4 b^2-c^2

Correct answer

B. c 4 4 a^2-c^2

Step-by-step solution

The area of triangle ABC is determined by analyzing the given conditions: a B = b A and a C c A . From the equation a B = b A , substituting the cosine rule B = a^2 + c^2 - b^2 2ac and A = b^2 + c^2 - a^2 2bc yields: a ( a^2 + c^2 - b^2 2ac ) = b ( b^2 + c^2 - a^2 2bc ) Simplifying gives a^2 + c^2 - b^2 = b^2 + c^2 - a^2 , leading to a^2 = b^2 . Since side lengths are positive, a = b , so the triangle is isosceles with sides a and b equal. The inequality a C c A is examined with a = b . Substituting C = 2b^2 - c^2

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