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Manipal MET2024MathematicsProperties of Triangles

In triangle A B C, A, B and C are in A P (C 90^ ) , then A is

Options

  1. A3 c-4 b 2 b
  2. B3 c-4 b 2 c
  3. C4 c-3 b 2 b
  4. D4 c-3 b 2 c

Correct answer

D. 4 c-3 b 2 c

Step-by-step solution

As we know, A a = B b = C c and A, B and C are in A P . So, a, b, c will also be in AP aligned 2 b & =a+c and A & = b^2+c^2-a^2 2 b c = b^2+c^2-(2 b-c)^2 2 b c & = b^2+c^2- (4 b^2+c^2-4 b c ) 2 b c & = -3 b^2+4 b c 2 b c & = b(4 c-3 b) 2 b c = 4 c-3 b 2 c aligned

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