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AP EAMCET201920 Apr 2019Evening ShiftMathematicsProperties of TrianglesActual

In A B C , if the median A D drawn through A is perpendicular to the side A C , then 3 c a A C+2 a^2=

Options

  1. Ac^2
  2. B2c^2
  3. C3c^2
  4. D4c^2

Correct answer

B. 2c^2

Step-by-step solution

According to Apollonius Theorem Now, 3 c a A C+2 a^2 aligned & =3 c a ( b^2+c^2-a^2 2 b c ) ( a^2+b^2-c^2 2 a b )+2 a^2 & = 3 4 b^2 [ (b^2+c^2-3 b^2-c^2 ) (3 b^2+c^2+b^2-c^2 ) ]+2 a^2 & = 3 4 b^2 (-2 b^2 ) (4 b^2 )+2 a^2=-6 b^2+2 a^2 & =2 (a^2-3 b^2 )=2 c^2 [from Eq. (iii)] aligned

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