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AP EAMCET2010MathematicsProperties of Triangles

In a A B C, C=90^ . Then, a^2-b^2 a^2+b^2 is equal to

Options

  1. A(A+B)
  2. B(A-B)
  3. C(A+B)
  4. D(A-B)

Correct answer

B. (A-B)

Step-by-step solution

C=90^ , a^2-b^2 a^2+b^2 ...(i) c= a^2+b^2-c^2 2 a b = 90^ a^2+b^2-c^2 2 a b =0a^2+b^2-c^2=0 c^2=a^2+b^2 From Eq. (i), we get a^2-b^2 a^2+b^2 = a^2-b^2 c^2 a A = b B = c C =R (constant) = (R A)^2-(R B)^2 (R C)^2 = ^2 A- ^2 B ^2 90^ ( 90^ =1 )=( A+ B)( A- B)=2 A+B 2 A-B 2 2 A+B 2 A-B 2 =2 4 A-B 2 2 4 A-B 2 A+B= -C= - 2 = 2 =2 2 1 2 1 2 A-B 2 A-B 2 =2 ( A-B 2 ) ( A-B 2 ) 2 A=2 A A= [2 (A-B) 2 ]= (A-B) Hence, a^2-b^2 a^2+b^2 = (A-B)

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