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MHT CET202522 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC with usual notations if, A 2 = b+c a , then the triangle A B C is

Options

  1. Aan isosceles triangle.
  2. Ban equilateral triangle.
  3. Ca right angled triangle.
  4. Dan obtuse angled triangle.

Correct answer

C. a right angled triangle.

Step-by-step solution

Given the condition in triangle ABC: A 2 = b + c a . Using the Law of Sines, a = 2R A , b = 2R B , c = 2R C , substitute into the equation: A 2 = B + C A . Apply sum-to-product and double-angle identities: B + C = 2 ( B + C 2 ) ( B - C 2 ) and A = 2 A 2 A 2 . From the angle sum A + B + C = , note that B + C 2 = - A 2 = 2 - A 2 , so ( B + C 2 ) = A 2 . Substitute and simplify: A 2 = 2 A 2 ( B - C 2 ) 2 A 2 A 2 = ( B - C 2 ) A 2 . Since A 2 = A 2 A 2 , equate: A 2 = ( B - C 2 ) . Given the domain constraints, A 2 = B

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