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KVPY2010MathematicsProperties of Triangles

Let ABC be a triangle and P be a point inside ABC such that PA +2 PB +3 PC = 0 . The ratio of the area of triangle ABC to that of APC is-

Options

  1. A2
  2. B3 2
  3. C5 3
  4. D3

Correct answer

D. 3

Step-by-step solution

PA +2 PB +3 PC =0( a - p )+2( b - p )+3( c - p )=0 p = a +2 b +3 c 6 array l Area ABC Area APC = 1 2 | a b + b c + c a | 1 2 | a p + p c + c a | put p = a +2 b +3 c 6 ratio =3 array

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