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AP EAMCET202318 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In ABC , if A , B , C are in arithmetic progression, then c a 2 ~A + a c 2 C =

Options

  1. A3 2
  2. B3
  3. C1
  4. D1 2

Correct answer

B. 3

Step-by-step solution

aligned & A, B, C are in A.P & 2 B=A+C & Now, A+B+C=180 3 B=180 B=60^ & c a 2 A+ a c 2 C= c a 2 A A+ a c 2 C C & =2 [ c a 2 b c (b^2+c^2-a^2 ) 2 b c + a c 2 a b a^2+b^2-c^2 2 a b ] aligned aligned & = 2 a b^2 c [b^2+c^2-a^2+a^2+b^2-c^2 ] & = 4 a c =2 B & =2 (60^ )=2 3 2 = 3 & ( c a 2 A+ a c 2 C )= 3 aligned

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