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AP EAMCET202418 May 2024Morning ShiftMathematicsProperties of TrianglesActual

If A B C, A+ B+ C=

Options

  1. A1+ r 2 R
  2. B1- r R
  3. C1+ R r
  4. D1+ r R

Correct answer

D. 1+ r R

Step-by-step solution

Since, A+ B+ C aligned & =2 ( C 2 ) ( A - B 2 )+1-2 ^2 ( C 2 ) & =1+2 ( C 2 ) ( ( A - B 2 )- ( C 2 ) ) aligned aligned & =1+2 ( C 2 ) ( ( A - B 2 )- ( A + B 2 ) ) & =1+2 ( C 2 ) 2 ( ~A 2 ) ( B 2 ) aligned aligned & =1+4 ( ~A 2 ) ( B 2 ) ( C 2 ) & =1+ r R Since, r=4 R ( A 2 ) ( B 2 ) ( C 2 ) aligned

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