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AP EAMCET2009MathematicsProperties of Triangles

In a A B C (a+b+c)(b+c-a)(c+a-b)(a+b-c) 4 b^2 c^2 equals

Options

  1. A^2 A
  2. B^2 B
  3. C^2 A
  4. D^2 B

Correct answer

C. ^2 A

Step-by-step solution

We know that, 2 s=a+b+c aligned & (a+b+c)(b+c-a)(c+a-b)(a+b-c) 4 b^2 c^2 & = 2 s(2 s-2 a)(2 s-2 b)(2 s-2 c) 4 b^2 c^2 & =4 s(s-a) b c (s-b)(s-c) b c & =4 ^2 A 2 ^2 A 2 = ^2 A & aligned

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