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AP EAMCET202319 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In ABC , a s - a + b s - b + c s - c =

Options

  1. A4 R r -1
  2. BR r -3
  3. C2 R r -1
  4. D4 R r -2

Correct answer

D. 4 R r -2

Step-by-step solution

aligned & a s-a + b s-b + c s-c & = a(s-b)(s-c)+b(s-a)(s-c)+c(s-a)(s-b) (s-a)(s-b)(s-c) aligned aligned & = s^2(a+b+c)-2 s(a b+b c+c a)+3 a b c (s-a)(s-b)(s-c) & = 2 s^3-2 s(a b+b c+c a)+2 a b c+a b c (s-a)(s-b)(s-c) & = a b c+2 [s^3-s(a b+b c+c a)+a b c ] (s-a)(s-b)(s-c) & = a b c-2(s-a)(s-b)(s-c) (s-a)(s-b)(s-c) & = a b c (s-a)(s-b)(s-c) -2 & = a b c s -2= 4 R r -2 [R= a b c , r= s ] aligned

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