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AP EAMCET202422 May 2024Morning ShiftMathematicsProperties of TrianglesActual

In A B C , if (a+c)^2=b^2+3 c a , then a+c 2 R =

Options

  1. A3 2
  2. B3 ( A-C 2 )
  3. C( A-C 2 )
  4. D( A-C 2 )

Correct answer

B. 3 ( A-C 2 )

Step-by-step solution

aligned & (a+c)^2=b^2+3 c a a^2+c^2-b^2=c a & B= a^2+c^2-b^2 2 a c = 1 2 = 60^ B 2 =30^ & a+c 2 R = A+ C=2 ( A+C 2 ) ( A-C 2 ) & =2 ( 2 - B 2 ) ( A-C 2 ) & =2 ( B 2 ) ( A-C 2 ) & =2 30^ ( A-C 2 )= 3 ( A-C 2 ) aligned

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