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AP EAMCET2013MathematicsProperties of Triangles

If in a A B C, 1 a+c + 1 b+c = 3 a+b+c , then C is equal to

Options

  1. A30^
  2. B45^
  3. C60^
  4. D90^

Correct answer

C. 60^

Step-by-step solution

In A B C 1 a+c + 1 b+c = 3 a+b+c Let C=60^ , then C= 3 aligned & a^2+b^2-c^2=a b & b^2+b c+a^2+a c=a b+a c+b c+c^2 & b(b+c)+a(a+c)=(a+c)(b+c) aligned Divide by (a+c)(b+c) and add 2 on both sides, we get aligned & 1+ b a+c +1+ a b+c =3 & 1 a+c + 1 b+c = 3 a+b+c aligned So, C should be 60^ .

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