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AP EAMCET202317 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In ABC , if C =90^ , then ( r ₁- r ₃ r ₁ ) ( r ₂- r ₃ r ₂ )=

Options

  1. A1
  2. B3
  3. C4
  4. D2

Correct answer

D. 2

Step-by-step solution

aligned & C=90^ C^2=a^2+b^2 & Now, ( r₁-r₃ r₁ ) ( r₂-r₃ r₂ )= s-a - s-c s-a s-b - s-c s-b & = s-c-(s-a) s-c s-c-(s-b) s-c & = a-c s-c b-c s-c = a b-a c-b c+c^2 ( a+b+c 2 -c )^2 & =4 (a b-a c-b c+a^2+b^2 ) (a+b-c)^2 & =4 (a b-a c-b c+a^2+b^2 ) a^2+b^2+c^2+2 a b-2 b c-2 c a & =4 a^2+b^2+a b-a c-b c 2 (a^2+b^2 )+2 a b-2 b c-2 c a =2 c^2=a^2+b^2 aligned

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