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KVPY2017MathematicsStraight Lines

Let ABC be an acute scalene triangle, and O and H be its circumcentre and orthocenter respectively. Further let N be the midpoint of OH. The value of the vector sum NA + NB + NC is

Options

  1. A0 (zero vector)
  2. BHO
  3. C1 2 HO
  4. D1 2 OH

Correct answer

C. 1 2 HO

Step-by-step solution

Circumcenter (origin O ) ( O )= ( a + b + c 3 ) ; H = ( a + b + c 2 ) N = 1 4 ( a + b + c )

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